Achieving high-performance dynamic behavior in a robot requires careful design of morphology. However, searching for a global optimum morphology in an intensely nonlinear design space is difficult, especially if stochastic seeding is used. In contrast to optimization, we encode design requirements into a polynomial system with a huge number of isolated roots. Each root describes an alternate robot morphology in the design space. Following this, the computation of nearly all isolated roots constitutes design space exploration. Previously, these systems were intractable, due to the heavy burden of degenerate roots. We relieve this burden by using the finite root generation (FRG) method to enable the discovery of nearly all isolated roots for a certain six-bar design problem for the first time. The FRG synthesis method enables the design of a transmission function from motor dynamics to a loaded end effector to influence the overall dynamic behavior. In an example, we formulate synthesis equations which were previously intractable, obtain 1 528 608 isolated roots (estimated 99.0%), and find 3764 physical designs. Design options are compared according to their sensitivity to joint errors.

Much current study of legged locomotion has rightly focused on foot traction forces, including on granular media. Future legged millirobots will need to go through terrain, such as brush or other vegetation, where the body contact forces significantly affect locomotion. In this work, a (previously developed) low-cost 6-axis force/torque sensing shell is used to measure the interaction forces between a hexapedal millirobot and a set of compliant beams, which act as a surrogate for a densely cluttered environment. Experiments with a VelociRoACH robotic platform are used to measure lift and drag forces on the tactile shell, where negative lift forces can increase traction, even while drag forces increase. The drag energy and specific resistance required to pass through dense terrains can be measured. Furthermore, some contact between the robot and the compliant beams can lower specific resistance of locomotion. For small, light-weight legged robots in the beam environment, the body motion depends on both legground and body-beam forces. A shell-shape which reduces drag but increases negative lift, such as the half-ellipsoid used, is suggested to be advantageous for robot locomotion in this type of environment.

The minimalist robot designs typically employed in swarms and teams can fall and get trapped when traversing irregular terrain. To protect against this contingency the design could add a specialized escape actuator, but each actuator drives up cost multiplicatively for the whole team. Instead, the emergency actuator can be found for free in the form of another teammate. Teammate pushing can be efficiently directed by careful shaping of the robot's exterior hull. This approach is illustrated by designing a shell for VelociRoACH robots that enables them to roll pronated comrades back onto their feet. The designed maneuver can be performed in open-loop with 87% success and an average time of 0.7 seconds.

Recent work in the design of mechanical systems for terrestrial locomotion has indicated successful strategies for increasing the energetic performance of a robotic locomotor without upgrading its actuator system. We apply one such strategy, termed power modulation, in a new way: for the design of a leg mechanism useful for running. Power modulation geometrically defines force/torque ratios between robot components to mechanically achieve certain energy transmission characteristics during fast stance dynamics that increase the kinetic power output of the overall system. Furthermore, we investigate the design of a leg mechanism that can adjust to exhibit power modulation. In this way, a leg mechanism would exhibit a low power mode for flat terrain, and can adjust to a high power mode for rough terrain. The latter makes jumping possible and extends the range of available footholds that can be accessed in a single step. To find a suitable leg mechanism, we leverage the Finite Root Generation method to compute a design. The design is advanced to a prototype and basic experiments are conducted to investigate its behavior as adjusted between high-and low-power modes.

Automatic repair of mechanical structures would enable a robot to recover or improve functions after physical damage. Little work exists on real-world execution of automatic repair in robotic systems. State-of-the-art takes a modular approach where the robotic system is modular and a replacement module is available. However, the modular approach suffers from low granularity in repair even with tens of motors. In addition, there is a lack of quantitative evaluation of the effect of automatic repair on robot functionality. Here we propose a cooperative method for automatic repair in a robotic system. Our method is regeneration-based rather than module-based and does not assume availability of a replacement part. It integrates a fabrication process on the fly for robot structure regeneration. With a system that consists of a regenerating robot, a legged robot and a pre-engineered ribbon, we demonstrate end-to-end execution of automated repair of the legged robot's leg by the regenerating robot in 335 seconds. Experiments on repeatability show a 100% success rate for sub-processes such as positioning, leg fabrication, and legged robot disengagement and a 90% success rate for leg detachment. We quantify the effect of leg regeneration on mobility recovery and found a 90% recovery of forward speed, a 19.7% increase of peak power and a 9.3% reduction of cost of transport with a regenerated leg.

OpenRoACH is a 15-cm 200-gram self-contained hexapedal robot with an onboard single-board computer. To our knowledge, it is the smallest legged robot with the capability of running the Robot Operating System (ROS) onboard. The robot is fully open sourced, uses accessible materials and off-the-shelf electronic components, can be fabricated with benchtop fast-prototyping machines such as a laser cutter and a 3D printer, and can be assembled by one person within two hours. Its sensory capacity has been tested with gyroscopes, accelerometers, Beacon sensors, color vision sensors, linescan sensors and cameras. It is low-cost within $150 including structure materials, motors, electronics, and a battery. The capabilities of OpenRoACH are demonstrated with multi-surface walking and running, 24-hour continuous walking burn-ins, carrying 200-gram dynamic payloads and 800-gram static payloads, and ROS control of steering based on camera feedback. Information and files related to mechanical design, fabrication, assembly, electronics, and control algorithms are all publicly available on https://wiki.eecs.berkeley.edu/biomimetics/Main/OpenRoACH.

We develop a drift-free roll and pitch attitude estimation scheme for monopedal jumping robots. The estimator uses only onboard rate gyroscopes and encoders and does not rely on external sensing or processing. It is capable of recovering from attitude estimate disturbances and, together with onboard velocity estimation, enables fully autonomous stable hopping control. The estimator performs well on a small untethered robot capable of large jumps and extreme stance accelerations. We demonstrate that the robot can follow a rectangular path using onboard dead-reckoning with less than 2 meters of drift over 200 seconds and 300 jumps covering 60 m. We also demonstrate that the robot can operate untethered outdoors under human wireless joystick direction.

Due to high impact forces and low duty cycles, monopedal jumping robots are particularly susceptible to failure from a slipping foot. Spines provide a solution to reduce slip, but there has been little research on how to effectively engage them into a surface with a dynamic jumping robot. Previous robots utilizing spines operate in different regimes of surface approach speed and cycle time. For a penetrable substrate, spines must be directed into the surface at suitable holding angles, then extracted before the foot leaves the ground. We accomplished this by designing a gripper mechanism for the robot Salto that pushes in angled spines along their length and is kinematically constrained to engage/disengage with leg crouch/extension. The resulting mechanism introduces no new actuators, enables jumping on penetrable inclines up to 60°, and enables static adhesion to hold 7.5 times the robot's weight from a ceiling.

Model-free deep reinforcement learning algorithms have been shown to be capable of learning a wide range of robotic skills, but typically require a very large number of samples to achieve good performance. Model-based algorithms, in principle, can provide for much more efficient learning, but have proven difficult to extend to expressive, high-capacity models such as deep neural networks. In this work, we demonstrate that neural network dynamics models can in fact be combined with model predictive control (MPC) to achieve excellent sample complexity in a model-based reinforcement learning algorithm, producing stable and plausible gaits that accomplish various complex locomotion tasks. We further propose using deep neural network dynamics models to initialize a model-free learner, in order to combine the sample efficiency of model-based approaches with the high task-specific performance of model-free methods. We empirically demonstrate on MuJoCo locomotion tasks that our pure model-based approach trained on just random action data can follow arbitrary trajectories with excellent sample efficiency, and that our hybrid algorithm can accelerate model-free learning on high-speed benchmark tasks, achieving sample efficiency gains of 3-5× on swimmer, cheetah, hopper, and ant agents. Videos can be found at https://sites.google.com/view/mbmf.

This paper analyzes and implements two novel turning strategies for underactuated legged robots that leverage contact of an active tail against terrain. The first strategy produces a sustained turn with a tail dragging against the ground during forward locomotion. The second strategy produces a rapid point turn by impacting the tail against the ground. LoadRoACH, a 55 g palm-sized legged robot, is developed to carry the active tail payload used in turning experiments. A steady-state turning model predicts the achievable turn speed of the robot on carpet, and open-loop turning experiments characterize the performance of the two tail contact turning strategies. Tail drag turning provides comparable turning maneuverability to differential drive turning gaits on carpet and gravel surfaces. Tail impact turning can produce rapid point turns on carpet, tarp, and gravel, but has a large variability in turn angle and time to recover from the turn. Finally, tail drag and tail impact turning control methods are implemented in an aggressive closed-loop corner steering maneuver.

Soft material robots are attractive for safe interaction with humans and unstructured environments due to their compliance and low intrinsic stiffness and mass. These properties enable new capabilities such as the ability to conform to environmental geometry for tactile sensing and to undergo large shape changes for actuation. Due to the complex coupling between sensing and actuation in high-dimensional nonlinear soft systems, prior work in soft robotics has primarily focused on either sensing or actuation. This paper presents SOFTcell, a novel controllable stiffness tactile device that incorporates both optical sensing and pneumatic actuation. We report details on the device's design and implementation and analyze results from characterization experiments on sensitivity and performance, which show that SOFTcell can controllably increase its effective modulus from 4.4kPa to 46.1kPa. Additionally, we demonstrate the utility of SOFTcell for grasping in a reactive control task in which tactile data is used to detect fingertip shear as a grasped object slips, and cell pressurization is used to prevent the slip without the need to adjust fingertip position.

Millirobots are a promising robotic platform for many applications due to their small size and low manufacturing costs. Legged millirobots, in particular, can provide increased mobility in complex environments and improved scaling of obstacles. However, controlling these small, highly dynamic, and underactuated legged systems is difficult. Hand-engineered controllers can sometimes control these legged millirobots, but they have difficulties with dynamic maneuvers and complex terrains. We present an approach for controlling a real-world legged millirobot that is based on learned neural network models. Using less than 17 minutes of data, our method can learn a predictive model of the robot's dynamics that can enable effective gaits to be synthesized on the fly for following user-specified waypoints on a given terrain. Furthermore, by leveraging expressive, high-capacity neural network models, our approach allows for these predictions to be directly conditioned on camera images, endowing the robot with the ability to predict how different terrains might affect its dynamics. This enables sample-efficient and effective learning for locomotion of a dynamic legged millirobot on various terrains, including gravel, turf, carpet, and styrofoam. Videos and further details can be found at https://sites.google.com/view/imageconddyn.

We developed a deadbeat foot placement hopping controller for an untethered monopedal robot, Salto-1P. The controller uses a third order Taylor series approximation to an offline dynamic model and performs well on the physical platform. The robot demonstrated precise foot placement even on trajectories with aggressive changes in speed, direction, and height: in a random walk, its error standard deviation was 0.10 m. We establish how foot placement precision is tightly limited by attitude control accuracy, requiring attitude error less than 0.7 degrees for some tasks. We also show how foot placement precision degrades linearly as hopping height increases. These precision results apply to the large class of controllers that prescribe touchdown angle to control running velocity.

This paper presents a novel manufacturing paradigm for constructing origami-inspired pop-up robots for future space exploration missions. The new approach uses a textile-enhanced rigid-flex printed circuit board (PCB) to implement a folding robot chassis using robust, spaceflight-tolerant materials, and integrates the robot electronics directly into the chassis for added compactness. The new approach also decouples the mechanical and electrical functions of the chassis flexures for improved kinematics and lifetime. This manufacturing paradigm was used to build PUFFER (Pop-Up Flat Folding Explorer Robot), a self-actuated pop-up rover being developed to provide a low-payload-cost mobility enhancement for future NASA missions.

In this paper we address the problem of multi-robot localization with a heterogeneous team of low-cost mobile robots. The team consists of a single centralized observer with an inertial measurement unit (IMU) and monocular camera, and multiple picket robots with only IMUs and Red Green Blue (RGB) light emitting diodes (LED). This team cooperatively navigates a visually featureless environment while localizing all robots. A combination of camera imagery captured by the observer and IMU measurements from the pickets and observer are fused to estimate motion of the team. A team movement strategy, referred to as inchworm, is formulated as follows: Pickets move ahead of the observer and then act as temporary landmarks for the observer to follow. This cooperative approach employs a single Extended Kalman Filter (EKF) to localize the entire heterogeneous multi-robot team, using a formulation of the measurement Jacobian to relate the pose of the observer to the poses of the pickets with respect to the global reference frame. An initial experiment with the inchworm strategy has shown localization within 0.14 m position error and 2.18° orientation error over a path-length of 5 meters in an environment with irregular ground, partial occlusions, and a ramp. This demonstrates improvement over a camera-only localization technique that was adapted to our team dynamic which produced 0.18m position error and 3.12° orientation error over the same dataset. In addition, we demonstrate improvement in localization accuracy with an increasing number of picket robots.

Legged robots can explore unstructured environments more effectively than wheeled robots, but high turning rate tracking is still a challenging problem, particularly on varying surfaces. Previous steering methods with small robots have shown high turn rates, but usually only on a limited set of surfaces. This paper proposes a new method for steering a miniaturized legged robot by cooperation between two robots connected by a compliant joint, creating a 73 gram, 12 legged robot. Detailed design issues and an empirical verification are presented for several cooperation strategies, including changing velocities of the 4 sets of leg triples. The robots use their combined traction forces to turn at better than 50 degrees/sec at 1 m/sec on various surfaces. Closed-loop steering using a differential drive strategy is implemented on the connected robots to track a “figure 8” trajectory on a tile surface.

As small legged robots for search and rescue are deployed in collapsed buildings with unstructured terrain and steep drop-offs, they run the risk of flipping over and becoming incapacitated. A single degree of freedom low-mass tail is added to a 77.5 g, 18 cm long VelociRoACH legged robot with protective shell, which gives it the capability to dynamically self-right. Quasi-static analysis of terrestrial self-righting gives design requirements for the tail actuator. Dynamic simulation predicts that terrestrial self-righting is slower than aerial self-righting with a massive tail, but can be achieved without adding significant mass away from the base of leg support. Open-loop experiments on terrain with varying friction and roughness show that VelociRoACH can dynamically self-right using tail contact in as little time as 256 ms. Finally, an autonomous self-righting experiment on an obstacle with multiple step drops demonstrates that the robot can detect inversion and rapidly self-right while walking on challenging terrain.

In this work we present a new robotic system, Salto-1P, for exploring extreme jumping locomotion. Salto-1P weighs 0.098 kg, and has an active leg length of 14.4 cm. The robot is able to perform a standing vertical leap of 1.25 m, continuously hop to heights over 1 m, and jump over 2 m horizontally. Salto-1P uses aerodynamic thrusters and an inertial tail to control its attitude in the air. A linearized Raibert step controller was sufficient to enable unconstrained in-place hopping and forwards-backwards locomotion with external position feedback. We present studies of extreme jumping locomotion in which the robot spends just 7.7% of its time on the ground, experiencing accelerations of 14 times earth gravity in its stance phase. An experimentally collected dataset of 772 observed jumps was used to establish the range of achievable horizontal and vertical impulses for Salto-1P.

Cooperation primitives for climbing steps were developed for a system of two 10 cm long VelociRoACH hexapedal legged robots with a removable connection. When performed sequentially, the set of primitives allow the team of two robots to climb a step on the order of their body length. These primitives use a tether between the robots actuated by a winch on one of the robots to form and release connections, run synchronously while connected, and provide a tether assist force while running. For a step with a coefficient of friction of 1 and a height of 6.5 cm, quasi-static analysis correctly predicts that the two connected robots can raise the front robot over the top of the step, while a single robot can only pitch upward against the step. The winch module designed to perform the cooperative climbing experiments meets the system goals of providing controllable forces greater than each robot's body weight while driving a removable connection between the robots. Experiments demonstrate that the robot system can perform each cooperation primitive individually with a reliability of at least 50% using simple strategies of maintaining a constant bounding frequency with the drive motors of each robot and a set tether tension with the winch.

In this paper, we propose a trajectory-adjustable integrated milli-scale jumping-crawling robot with improved ability to overcome obstacles compared to a robot that can only crawl. The robot employs a novel jumping module with enhanced energy storing-capacity and a height-adjustable active trigger. To increase the energy-storing capacity, latex rubber and knee-like joints are employed to utilize large displacement of the elastic material. The active trigger is based on a single DC motor and can release stored energy at any state, enabling the robot to control the take-off speed of jumping. The jumping module is integrated with the lightweight Dash crawler. The integrated jumping-crawling robot weighs 59.4 g and controls its moving trajectory by adjusting both its crawling speed and its jumping take-off speed.

Automatic folding has drawn increasing attention in robotics research in the past ten years. The focus has been on folding two-dimensional (2D) sheets into three-dimensional (3D) structures, but little work has been done on how structures may be formed by folding ribbons. Here we propose the concept of robotic ribbon folding including a general workflow from shape design to ribbon folding and shape retention. We also propose a method to realize robotic ribbon folding on the macroscopic scale. The method consists of minimally engineered ribbons with patterned flexures, a folding robot, and a folding scheme that relates the orientation of flexures, the type of folds and the type of structural elements. By using this method we demonstrate robotic ribbon folding into 2D static structures such as triangles and squares, 3D static structures, and planar kinematic linkages such as a simple non-crossing four-bar mechanism. Burn-in result shows a four-bar mechanism with all bars' length of 5 cm could move for over 660 cycles.

Animals and robots alike face challenges of flipping-over as they move in complex terrain. Small insects like cockroaches can rapidly right themselves when upside down, yet small fast-running legged robots are much less capable of ground-based self-righting. Inspired by the discoid cockroach that opens its wings to push against the ground to self-right, we designed actuated wings for robot self-righting based on recently-developed rounded shells for obstacle traversal [1]. We measured the self-righting performance of a robot using these actuated wings, and systematically studied the effects and trade-offs of wing opening magnitude, speed, symmetry, and wing geometry. Our study provided a proof-of-concept that robots can take advantage of an existing body structure (rounded shell) in novel ways (as actuated wings) to serve new locomotor functions, analogous to biological exaptations [2]. Our results demonstrated that the robot self-rights dynamically, with active wing pushing followed by passive falling, and benefits from increasing kinetic energy by pushing faster and longer. Our experiments also showed that opening both wings asymmetrically increases righting probability at low wing opening magnitudes.

New work in robotics targets the development of controllable agile motions such as leaping. In this work, we examine animal and robotic systems on the metric of jumping agility and find that animals can outperform the most agile robots by a factor of two. These specially adapted animals use a jumping strategy we term power modulation to generate more peak power for jumping than otherwise possible. A novel eight-bar revolute mechanism designed with a new linkage synthesis approach encodes the properties for power modulation as well as constraints which assure rotation-free jumping motion. We fabricate an 85 gram prototype and demonstrate that it can perform a range of jumps while constrained by a linear slide. The prototype can deliver 3.63 times more peak jumping power than the maximum its motor can produce. A simulation matched to the physical parameters of the prototype predicts that the robot can attain an agility exceeding that of the most agile animals if the actuator power is increased to 15W.

Ribbon folding is a new approach to structure formation that forms higher dimensional structures using a lower dimensional primitive, namely a ribbon. In this paper, we present a novel algorithm to address path planning for ribbon folding of multi-link planar structures. We first represent the desired structure with a graph-based representation of edges and nodes. We then use graph theory to claim that for any object which is represented by a connected graph, there exists a continuous path which visits all of its edges. Finally, we develop a path planning algorithm that takes into account the physical constraints of the folding machine. The input is the desired planar structure, and the output is the optimal sequence of ribbon folds for creating that structure using the minimum number of folds. The results of this algorithm are successfully used to fold various planar structures.

This paper details a method for identifying a set of piece-wise affine linear models that can be used for control design for flapping-winged flight. The paper focuses on diving maneuvers as the application for these models. The flight conditions during the dive are segmented into separate dynamically similar regions, and least-squares is used to estimate affine linear models for each modeling region. These models are used to compute the reachability sets that satisfy recovery conditions for safe diving. The point within the dive to begin recovery was determined by checking the current pose for inclusion in the backward reachable set. Using this control method, 2.2 meter dives were achieved at a success rate of 60 percent. The data-driven automatic modeling techniques and controller design processes can be extended to additional flight maneuvers, provided sufficient previous data have been collected for model generation of those maneuvers.

The X2-VelociRoACH is a 54 gram experimental legged robot which was developed to test hypotheses about running with unnaturally high stride frequencies. It is capable of running at stride frequencies up to 45 Hz, and velocities up to 4.9 m/s, making it the fastest legged robot relative to size. The top speed of the robot was limited by structural failure. We present new methods and materials to make more robust folded robotic structures. High-frequency running experiments with the robot shows that the power required to cycle its running appendages increase cubically with the stride rate. Our findings show that although it is possible to further increase the maximum velocity of a legged robot with the simple strategy of increasing stride frequency, considerations must be made for the energetic demands of high stride rates.

Collapsible leg spines found on insects and spiders provide a passive mechanism for increased traction while running over complex terrain. In this paper we use this architectural advantage as biological inspiration to increase the useful work in pulling a load with a VelociRoACH, a high speed terrestrial robot. These spines exhibit anisotropic properties in the fore-aft and lateral directions, with a 2:1 holding-to-release force ratio on corkboard (0.2 N to 0.1 N). This increase in effective friction coefficient at the foot-to-surface contact points has decreased the Cost of Pulling for the VelociRoACH by ten times, allowing it to transport loads using less energy. The VelociRoACH with spines is able to engage the surface and pull up to 0.36 N whereas without spines it slips while pulling 0.2 N, demonstrating that the robot's performance with spines is now torque limited rather than friction limited. The spines also allow the robot to remain dynamically stable and resist torque disturbances.

In this work, we develop a cooperative launching system for a 13.2 gram ornithopter micro-aerial vehicle (MAV), the H2Bird, by carrying it on the back of a 32 gram hexapedal millirobot, the VelociRoACH. We determine the necessary initial velocity and pitch angle for take off using force data collected in a wind tunnel and use the VelociRoACH to reach these initial conditions for successful launch. In the wind tunnel predicted success region, we were able to complete a successful launch for 75 percent of the 12 trials in that region. Although carrying the H2Bird on top of the VelociRoACH at a stride frequency of 17 Hz increases our average power consumption by about 24.5 percent over solo running, the H2Bird, in turn, provides stability advantages to the VelociRoACH. We observed that the variance in pitch and roll velocity with the H2Bird is about 90 percent less than without. Additionally, with the H2Bird flapping at 5 Hz during transport, we observed an increase of 12.7 percent of the steady state velocity. Lastly, we found that the costs of transport for carrying the H2Bird flapping and without (6.6 and 6.8) are lower than the solo costs of transport for the VelociRoACH and for the H2Bird (8.1 and 10.1).

Mobile robot contact sensing can be useful for navigation and manipulation with small robots. In this work, we present a low-cost, 18.7 gram force-torque sensor for a 10 cm hexapedal millirobot. A planar array of photo interrupters, rigidly attached to the structure of the robot, is used to measure the six-axis movement of a shell attached to the robot with springs. The sensors measure the intensity of infrared light reflected off of a surface on the underside of the shell, which has been specially designed to enable the resolution of the forces and moments in the x-, y-, and z-axes applied to the shell. The sensor has a force sensitivity of 17 mN and torque sensitivity of 0.72 mN-m for a sampling rate of 100 Hz. The sensor can resolve a force equivalent to 2.9% of the combined robot and sensor weight of 581 mN.

This paper presents “1STAR,” which is the first robot that is driven by a single actuator but can be directly commanded to move straight or turn clockwise or counterclockwise. The legged robot relies on a novel actuation gait, which exploits the compliance disparity between alternate stance tripods, to generate rotation by continuously accelerating and decelerating the legs. The direction of turning depends on the configuration of the legs-tripod left or right-and the timing of the acceleration and deceleration. Alternating leg acceleration in successive steps allows for continuous rotation in the desired direction. The turning radius can be varied by changing the timing of the leg acceleration and deceleration without changing the cycle frequency and linear speed. A simplified kinematic motion model of a robot is presented, and a dynamic simulation is performed to analyze the behavior and optimize robot parameters. The locomotion gait is verified experimentally using our newly designed “1STAR” robot.

As we seek to develop more maneuverable legged robots, we need to understand the dynamics of legged turning in an approachable fashion. In this work, we analyze the dynamic turning motion of a dynamic hexapedal millirobot. We explore a family of phase locked turning gaits where all legs of the robot move at the same speed. These gaits are highly periodic, allowing the vertical height and roll angle of the robot to be approximated by single harmonic sinusoidal functions. We demonstrate that oscillations in height and roll angle determine the robot's turning behavior. The phase between these oscillations (and therefore the turning behavior) was modulated by the phase between the left and right sets of legs. A simple model using compliant leg forces was shown to match turning behavior for a range of 5Hz turning gaits. Based on the finding that roll oscillations are major determinants of turning behavior, we modified the robot to create a new high speed turning gait (forward velocity: 0.4 m/s, turn rate 206°/s).

Legged robots come in a range of sizes and capabilities. By combining these robots into heterogeneous teams, joint locomotion and perception tasks can be achieved by utilizing the diversified features of each robot. In this work we present a framework for using a heterogeneous team of legged robots to detect slippery terrain. StarlETH, a large and highly capable quadruped uses the VelociRoACH as a novel remote probe to detect regions of slippery terrain. StarlETH localizes the team using internal state estimation. To classify slippage of the VelociRoACH, we develop several Support Vector Machines (SVM) based on data from both StarlETH and VelociRoACH. By combining the team's information about the motion of VelociRoACH, a classifier was built which could detect slippery spots with 92% (125/135) accuracy using only four features.

Developing models of flapping-winged fliers in free flight is vital for accurate control. The aerodynamics associated with flapping-winged flight are complex. Hence, a look-up table flight force model from wind tunnel data is a practical approach. In this work, we compare the flight of an ornithopter micro aerial vehicle (MAV), using free flight data collected from a Vicon motion capture system, to measured wind tunnel force and moment values. We compare the two data sets at equilibrium as a metric to determine the quality of the wind tunnel flight force estimation. To compare the two data sets, we find the predicted equilibrium angle of attack and velocity for the ornithopter in free flight. For a given flapping frequency and pitch control elevator deflection angle at free flight equilibrium, we compute the level sets at zero for pitch moment, net horizontal force, and net vertical force from the wind tunnel data. We then use the point on the zero moment level set that minimizes the vertical and horizontal force. The angle of attack and velocity at this minimal point are the wind tunnel predicted equilibrium point and are compared to the analogous free flight equilibrium point. We determined that the wind tunnel underestimates the angle of attack of the equilibrium point observed in free flight by 15 degrees, while the equilibrium velocity has an error of 0.1 m/s between the two sets at an average flight speed of 2 m/s.

We present a novel dynamic gait to control in-plane locomotion [1] (forward, back, clockwise and counter clockwise rotations) of a compliant legged hexapedal robot using a single actuator. The gait exploits the compliance disparity between alternate stance tripods, to generate rotation by controlling the acceleration of the robot [2]. The direction of turning depends on the configuration of the legs- tripod left or right- and the direction of the acceleration. Alternating acceleration in successive steps allows for continuous rotation in the desired direction. A simplified model of a robot is made and a numerical simulation was performed to analyze the behavior and optimize robot parameters. The robot is capable of rotating with a coefficient of friction as low as 0.2 but its performance improves as the COF increases up to 0.6. Beyond that, little change is noticed.

We present our findings on the first application of motion planning methodologies to the recently introduced Sprawl Tuned Autonomous Robot (STAR). The reported results provide a first glimpse on the capabilities of this novel, 3D-printed robot in performing autonomously non-trivial motion planning tasks in environments populated with obstacles. We employ methods from sampling-based motion planning under nonholonomic constraints, and implement in open loop the generated path on the physical robot for various environments of increasing complexity.

The VelociRoACH is a 10 cm long, 30 gram hexapedal millirobot capable of running at 2.7 m/s, making it the fastest legged robot built to date, relative to scale. We present the design by dynamic similarity technique and the locomotion adaptations which have allowed for this highly dynamic performance. In addition, we demonstrate that rotational dynamics become critical for stability as the scale of a robotic system is reduced. We present a new method of experimental dynamic tuning for legged millirobots, aimed at finding stable limit cycles with minimal rotational energy. By implementing an aerodynamic rotational damper, we further reduced the rotational energy in the system, and demonstrated that stable limit cycles with lower rotational energy are more robust to disturbances. This method increased the stability of the system without detracting from forward speed.

For maximum maneuverability, terrestrial robots need to be able to turn precisely, quickly, and with a small radius. Previous efforts at turning in legged robots primarily have used leg force or velocity modulation. We developed a palm-sized legged robot, called TAYLRoACH. The tailed robot was able to make rapid, precise turns using only the actuation of a tail appendage. By rapidly rotating the tail as the robot runs forward, the robot was able to make sudden 90° turns at 360 °s-1. Unlike other robots, this is done with almost no change in its running speed. We have also modeled the dynamics of this maneuver, to examine how features, such as tail length and mass, affect the robot's turning ability. This approach has produced turns with a radius of 0.4 body lengths at 3.2 body lengths per second running speed. Using gyro feedback and bang-bang control, we achieve an accuracy of ± 5° for a 60° turn.

In this work we analyze the cost of transport of in-plane hexapedal robots. The robots are modeled as a rigid body with six massless legs, each having two compliant degrees of freedom and the contact is modeled using Coulomb's model. We start our analysis by formulating the cost of transport for rigid legged robots as a function of their geometry, friction coefficients, actuation velocities and slope angle and compare it to the results of a dynamic multibody numeric simulation. In the second part, we estimate the cost of transport in the more general case when the legs and surface are compliant. We evaluate the energy consumptions factors, sliding, work against gravity, elastic losses of the legs and the surface, and kinetic energy and compare them to the total energy input of the actuators. This analysis allows us to evaluate the work range of the robots and determine the optimum locomotion paths for improved battery performance.

This paper presents a six-legged, sprawl-tuned autonomous robot (STAR). This novel robot has a variable leg sprawl angle in the transverse plane to adapt its stiffness, height, and leg-to-surface contact angle. The sprawl angle can be varied from nearly positive 60 degrees to negative 90 degrees, enabling the robot to run in a planar configuration, upright, or inverted (see movie). STAR is fitted with spoke wheel-like legs which provide high electromechanical conversion efficiency and enable the robot to achieve legged performance over rough surfaces and obstacles, using a high sprawl angle, and nearly wheel-like performance over smooth surfaces for small sprawl angles. Our model and experiments show that the contact angle and normal contact forces are substantially reduced when the sprawl angle is low, and the velocity increases over smooth surfaces, with stable running at all velocities up to 5.2m/s and a Froude number of 9.8.

Abstract — This paper presents a simple, data-driven tech-nique for identifying models for the dynamics of legged robots. Piecewise Affine (PWA) models are used to approximate the observed nonlinear system dynamics of a hexapedal millirobot. The high dimension of the state space (16) and very large number of state observations (∼100,000) motivated the use of statistical clustering methods to automatically choose the submodel regions. Comparisons of models with 1 to 50 PWA regions are analyzed with respect to state derivative prediction and forward simulation accuracy. Derivative prediction accu-racy was shown to reduce average in-axis absolute error by up to 52 % compared to a null estimator. Simulation results show tracking of state trajectories over one stride length, and the degradation of simulation prediction is analyzed across model complexity and time horizon. We describe metrics for comparing the performance of different model complexities across one-step and simulation predictions. I.

Turning while running at high speeds remains a difficult task for legged robots, but this capability is crucial for maneuvering quickly in a real-world environment. In this work we present a 10 cm long novel robot, SailRoACH, the first running robot that uses aerodynamic forces to turn. We present a scale analysis of aerodynamic steering, showing this steering method is most effective for small robots. Modeling and simulations were performed, and validated with experiments, that showed the robot is capable of stably turning in a 1.2 m radius at 1.6 ms-1. We also show that aerodynamic steering is superior for high speed turns at high forward velocity, compared to existing methods. Additionally, aerodynamic steering allows us to introduce a constant yaw disturbance to the robot. This is useful for studying legged locomotion, and is difficult to achieve otherwise.

Rapid and consistent turning of running legged robots on surfaces with moderate friction is challenging due to leg slip and uncertain dynamics. A tail is proposed as a method to effect turns at higher yaw frequencies than can be obtained by differential velocity drive of alternate sides. Here we introduce a 100 mm scale dynamic robot - OctoRoACH - with differential-drive steering and a low-mass tail to investigate issues of yaw rate control. The robot without tail is underactuated with only 2 drive motors and mass of 35 grams including battery and control electronics. For some surface conditions, OctoRoACH can maintain heading or turning rate using only leg velocity control, and a basic rate-gyro-based heading control system can respond to disturbances, with a closed-loop bandwidth of approximately 1 Hz. Using a modified off-the-shelf servo for the tail drive, the robot responds to turning commands at 4 Hz and up to 400°/sec.

Minimally actuated millirobotic crawlers navigate unreliably over uneven terrain-even when designed with inherent stability-mostly because of manufacturing variabilities and a lack of good models for ground interaction. In this paper, we investigate the performance of a legged robot as it traverses three distinct rough terrains: tile, carpet, and gravel. Furthermore, we present an accurate, robust, low-lag, and efficient algorithm for terrain classification that uses vibration data from the on-board inertial measurement unit and motor control data from back-EMF sensing and magnetic encoders.

A 10 cm hexapedal robot is adapted to dynamically climb near-vertical smooth surfaces. A gecko-inspired adhesive is mounted with an elastomer tendon and polymer loop to a remote-center-of-motion ankle that allows rapid engagement with the surface and minimizes peeling moments on the adhesive. The maximum velocity possible while climbing decreases as the incline gets closer to vertical, with the robot able to achieve speeds of 10 cm second-1at a 70-degree incline. A model is implemented to describe the effect of incline angle on climbing speed and, together with high-speed video evidence, reveals that climbing velocity is limited by robot dynamics and adhesive properties and not by power.

This work presents a low-complexity modular sensor grid architecture to provide a smart skin to non-convex shapes, such as a robot body and legs. To configure a sensing skin shaped by arbitrary cuts and rapid changes in designs, we use a wavefront planning approach to generate a minimum-depth spanning tree of an arbitrary topology of contiguous, regularly arranged modular sensing units on a flexible substrate wired network. A Finite State Machine protocol for extracting this topology and sensor information is shown that is robust to destructive sensor loss, device failure, and transmission noise. The architecture is designed to require as little state complexity at each node as possible to minimize the area and cost of such a network implemented in printable semiconductor technology. Simulation data show recovery from network failures and extension of the architecture to larger networks with arbitrary geometry, and a sample synthesis of the verified architecture logic is shown to have a very low state and combinational logic complexity. A proof-of-concept implementation of the architecture using microcontrollers and optical proximity sensors on a flexible substrate show integration with a Scaled Composite Manufacturing process used for Biomimetic Millirobots.

We present a rapid-manufacturable, hair-actuated contact sensor array designed for use on legged millirobots. The sensor is an array of sensitive contact switches. Each switch is activated by loading a hair mounted at the switch tip. The hair sensor array is sufficiently sensitive to detect the small contact forces experienced by a lightweight robot, with an average normal sensitivity of 0.8 grams/hair. The compliant polymer hairs detect both normal and shear contact, allowing the array to detect a variety of contact forces. By virtue of its design, the hair sensor array can be fabricated using a roll-to-roll layered process. We demonstrate a straightforward application of the sensor technology on a hexapedal millirobot, using the array to both estimate average ground speed and detect high-centering when running over obstacles. This application is of particular interest for milliscale robots operating in rough terrain, where the risk of entrapment is high. Our results indicate that the hair sensor array can estimate ground speed and detect high-centering when running over simple geometric obstacles.

This paper proposes a novel dynamic gait of locomotion for hexapedal robots which enables them to crawl forward, backward, and rotate using a single actuator. The gait exploits the compliance difference between the two sides of the tripods, to generate clockwise or counter clockwise rotation by controlling the acceleration of the robot. The direction of turning depends on the configuration of the legs -tripod left of right- and the direction of the acceleration. Alternating acceleration in successive steps allows for continuous rotation in the desired direction. An analysis of the locomotion is presented as a function of the mechanical properties of the robot and the contact with the surface. A numerical simulation was performed for various conditions of locomotion. The results of the simulation and analysis were compared and found to be in excellent match.

This work presents the design, fabrication, capabilities, and obstacle traversal mechanics of MEDIC (Millirobot Enabled Diagnostic of Integrated Circuits), a small legged robot able to overcome a varied array of obstacles. MEDIC features a hull that keeps its body in contact with the ground at all times, and uses only four actuators to move forward, turn, mount obstacles, and move in reverse. The chassis is fabricated using a Smart Composite Microstructures (SCM) approach and the robot is actuated by coiled Shape Memory Alloy (SMA). MEDIC also features a camera which will be useful for navigation in the future.

Recent advances in small-scale flapping-wing micro aerial vehicles have extended the capabilities of flight control for a number of applications, such as intelligence, surveillance, and reconnaissance activities. In this work, we demonstrate autonomous flight control of a 13 gram ornithopter capable of flying toward a target without remote assistance. For autonomous flight control, we developed 1.0 gram control electronics integrated with a microcontroller, inertial and visual sensors, communication electronics, and motor drivers. We also developed a simplified aerodynamic model of ornithopter flight to reduce the order of the control system. With the aerodynamic model and the orientation estimation from on-board inertial sensors, we present flight control of an ornithopter capable of flying toward a target using onboard sensing and computation only. To this end, we developed a dead-reckoning algorithm to recover from the temporary loss of the target which can occur with a visual sensor with a narrow field of view. As a result, the 28 cm wing-span ornithopter flying toward a target landed within a radius of 0.5 m from the target with more than 85% success (N = 20).

CLASH is a 10cm, 15g robot capable of climbing vertical loose-cloth surfaces at 15 cm per second. The robot has a single actuator driving its six legs which are equipped with novel passive foot mechanisms to facilitate smooth engagement and disengagement of spines. These foot mechanisms are designed to be used on penetrable surfaces and offer improved tensile normal force generation during stance and reduced normal pull-off forces during retraction. Descended from the DASH hexapedal robot, CLASH features a redesigned transmission with a lower profile and improved dynamics for climbing. CLASH is the first known robot to climb loose vertical cloth and is able to climb surfaces when surface rigidity is not guaranteed.

BOLT is a lightweight bipedal ornithopter capable of high-speed dynamic running and effecting transitions between aerial and terrestrial locomotion modes. The gait dynamics of both quasi-static and dynamic locomotion are examined through the use of an on-board accelerometer, part of a one gram electronics package also containing a processor and radio. We discuss the accelerations in the context of the traditional spring-loaded inverted pendulum model seen in nearly all legged locomotion in organisms. Flapping wings are shown to provide damping along with propulsive force. The aerodynamic forces of the flapping wings also impart passive stability to the robot, enabling it to run bipedally with only a single actuator. BOLT transitions from ground running to aerial hovering in as little as one meter of runway. Overall, the advantages provided by wings in terrestrial locomotion, coupled with aerial capabilities, allow BOLT to navigate complex three dimensional environments, switching between locomotion modes when necessary.

Flapping-wing air vehicles can improve efficiency by running at resonance to reduce inertial costs of accelerating and decelerating the wings. For battery-powered, DC motor-driven systems with gears and cranks, the drive torque and velocity is a complicated function of battery voltage. Hence, resonant behavior is not as well defined as for flapping-wing systems with elastic actuators. In this paper, we analyze a resonant drive to reduce average battery power consumption for DC motor-driven flapping-wing robots. We derive a nondimensionalized analysis of the generic class of a motor-driven slider crank, considering motor and battery resistance. This analysis is used to demonstrate the benefits of efficient resonant drive on a 5.8 g flapping-wing robot and experiments showed a 30% average power reduction by integrating a tuned compliant element.

Optical flow sensing techniques are promising for obstacle avoidance, distance regulation, and moving target tracking, particularly for small mobile robots with limited power and payload constraints. Most optical flow sensing experimental work has been done on mobile platforms which are relatively steady in rotation, unlike the pitching motion expected on flapping wing flyers. In order to assess the feasibility of using optical flow to control an indoor flapping flyer, an 7 gram commercially available ornithopter airframe was equipped with on-board camera and CPU module with mass of 2.5 grams and 2.6 gram battery. An experiment was conducted capturing optical flow information during flapping and gliding flight on the same platform. As expected, flapping introduced substantial systematic bias to the direction estimates to the point of flipping the true direction periodically. Nonetheless, since the optical flow results oscillated at the same frequency as the flapping wings, it is envisioned that one could disambiguate the jittering optic flow measurements by correlating these with real-time feedback from the motor current.

DASH, or the dynamic autonomous sprawled hexapod, is a small, high-power density, minimally actuated robot capable of high-speed running and surviving large falls. The design of DASH has been informed by the study of nature's greatest runners from whom scientists have derived many models for robust high-speed locomotion. DASH is constructed using a scaled smart composite manufacturing (SCM) process which creates rigid cardboard beams with flexible polymer joints that can be folded into complex functional elements. DASH utilizes an alternating tripod gait, and the mechanism by which it creates an alternating tripod gait from a single DC motor is presented. DASH is 10 cm long, has a mass of 16.2 grams, and is capable of running straight at speeds of 1.5 m/s, or 15 body-lengths per second, which is as fast as other similar legged runners in body-lengths per second. Both real time and slow-motion video of high-speed running are shown. A lightweight servomotor can modify the kinematics of DASH so that turning moments are generated. The cardboard beams from which DASH is constructed are rigid in directions which allow for sufficient power transmission for high-speed running. The beams are also flexible but resilient to off-aixs forces and moments which allow DASH to contort and absorb energy under forces not normally seen during running. This property helps to enable DASH survive large falls without damage, including drops from 28 meters onto concrete.

DASH is a small, lightweight, power autonomous robot capable of running at speeds up to 15 body lengths per second (see video). Drawing inspiration from biomechanics, DASH has a sprawled posture and uses an alternating tripod gait to achieve dynamic open-loop horizontal locomotion. The kinematic design which uses only a single drive motor and allows for a high power density is presented. The design is implemented using a scaled Smart Composite Manufacturing (SCM) process. Evidence is given that DASH runs with a gait that can be characterized using the spring-loaded inverted pendulum (SLIP) model. In addition to being fast, DASH is also well suited to surviving falls from large heights, due to the uniquely compliant nature of its structure.

We present an approach to quantifying the off-axis stiffness properties of parallel compliant mechanisms used in the design of mobile millirobots. By transforming the stiffness of individual flexure elements and rigid links comprising a compliant mechanism into a global coordinate system, we enable the formulation of an equivalent mechanism stiffness. Using that stiffness in concert with an energy-based performance metric, we predict the performance of a compliant mechanism subjected to a prescribed set of forces in the global coordinate system. We analyze a flexure-based Sarrus linkage and use the performance metric to improve the design by adding topological redundancy. Finally, our approach is experimentally validated by constructing and testing SCM Sarrus linkages in a variety of geometries and topologies and demonstrating agreement between the model and our experiments.

We present a set of tools and a process, making use of inexpensive and environmentally friendly materials, that enable the rapid realization of fully functional large scale prototypes of folded mobile millirobots. By mimicking the smart composite microstructure (SCM) process at a 2-10X scale using posterboard, and commonly available polymer films, we can realize a prototype design in a matter of minutes compared with days for a complicated SCM design at the small scale. The time savings enable a significantly shorter design cycle by allowing for immediate discovery of design flaws and introduction of design improvements prior to beginning construction at the small scale. In addition, the technology eases the difficulty of visualizing and creating folded 3D structures from 2D parts. We use the example of a fully functional hexapedal crawling robot design to illustrate the process and to verify a scaling law which we propose.

We present a set of tools and a process, making use of inexpensive and environmentally friendly materials, that enable the rapid realization of fully functional large scale prototypes of folded mobile millirobots. By mimicking the smart composite microstructure (SCM) process at a 2–10X scale using posterboard, and commonly available polymer films, we can realize a prototype design in a matter of minutes compared with days for a complicated SCM design at the small scale. The time savings enable a significantly shorter design cycle by allowing for immediate discovery of design flaws and introduction of design improvements prior to beginning construction at the small scale. In addition, the technology eases the difficulty of visualizing and creating folded 3D structures from 2D parts. We use the example of a fully functional hexapedal crawling robot design to illustrate the process and to verify a scaling law which we propose.

In this work, we explore the mechanical behavior of gecko hairs by means of macromodels. The macromodel has four spatular hairs operating by magnetic forces instead of van der Waals forces. The purpose of the models is to simulate the mechanics of the actual gecko seta. For additional hair compliance, a two degree of freedom double bent spatular hair geometry is chosen. A mathematical model for the displacement and forces (slide, peel, and pull-off) for the macro scale gecko hairs is presented. Experiments showed good agreement with the model and a directional adhesion effect which could be useful for locomotion.

This work presents the design, fabrication, and testing of a novel hexapedal walking millirobot using only two actuators. Fabricated from S2-glass reinforced composites and flexible polymer hinges using the smart composite microstructures (SCM) process, the robot is capable of speeds up to 1 body length/sec or approximately 3 cm/s. All power and control electronics are onboard and remote commands are enabled by an IrDA link. Actuation is provided by shape memory alloy wire. At 2.4 g including control electronics and battery, RoACH is the smallest and lightest autonomous legged robot produced to date.

We describe the design, fabrication, and testing of an ultra-low cost orthotweezers system for microassembly. By utilizing rapid prototyping technology, compliant mechanisms, and commodity-grade actuators and sensors, we significantly reduce the complexity and cost of the previous Orthotweezers system without sacrificing functionality. With a force resolution of 0.7mN and a worst case mean positioning repeatability of 23 mum, the system is capable of dexterously manipulating rectangular parts with dimensions 200 mum times 200 mum times 100 mum. Such blocks can then be temporarily attached to thin, delicate, or oddly shaped parts to enable handling and ultimately assembly of micromechanical structures. Strategies for using compliance to compensate for uncertainty introduced by less expensive fabrication methods, actuators, and sensors are also discussed.

The Micromechanical Flying Insect (MFI) project aims to create a 25 mm (wingtip to wingtip) flapping wing micro air vehicle inspired by the aerodynamics of insect flight. A key challenge is generating appropriate wing trajectories. Previous work showed a lift of 506muN at 160 Hz using feedforward control. In this paper, refinements to the MFI design including those in [2] increased wing beat frequency to 275 Hz and lift to 1400muN using pure sinusoidal drive for a fixed benchtop experiment. We show through simplified aerodynamic models that not only do sinusoidal actuator drives produce close to maximal lift, but significantly improved wing trajectories due to non-sinusoidal actuator drives are practically unobtainable due to actuator limitations.

Piezoelectric bending actuators are an attractive option for driving microrobots due to their light weight, scalability, ease of integration and high bandwidth. However, the only existing energy or power output measurements for piezoelectric bending actuators have been extrapolated from DC values or unloaded AC values and are most likely overestimates. For microrobot applications such as flapping flight, accurate measures of power density are critical. In this work, to properly measure the energy output of a lOmg piezoelectric actuator, a custom dynamometer is designed and constructed to directly measure the power output at various frequencies and conditions. The dynamometer can simulate a pure resistive load at resonant frequencies from 1 to 100Hz. Due to low internal damping and fracture limits, actuators cannot be run in the matched condition at high fields (> 1 V/mum). Using the device, energy output per cycle at 1.6 V/mum was measured to be a maximum of 19.1muJ/cycle (232mum amplitude, 30Hz), giving a delivered energy density per cycle of 1.89J/kg. Internal actuator damping was measured at 1 V/mum to account for an energy loss of only 0.21muJ per cycle (232mum amplitude, 30Hz).

Compliant mechanisms provide an attractive alternative to conventional rigid mechanisms in the design of ultra low-cost precision positioning systems. The desirable performance characteristics of these mechanisms including freedom from backlash, long life, light weight, and ease of fabrication/assembly make them an ideal solution to the problem of inexpensive precision positioning for microassembly. This paper presents a design for a 2 axis precision positioning system which makes use of large displacement compliant mechanisms, a room temperature and pressure molding fabrication process, commodity hardware, and a piecewise linear interpolation compensation scheme to achieve positioning performance suitable for automated assembly of sub-centimeter robotic and mechatronic devices

This paper discusses the biomimetic design and assembly of a 3g self-contained crawling robot fabricated through the integrated use of various microrobot technologies. The hexapod structure is designed to move in an alternating tripod gait driven by two piezoelectric actuators connected by sliding plates to two sets of three legs. We present results of both the kinematic and static analyses of the driving mechanism that essentially consists of three slider cranks in series. This analysis confirmed the force differential needed to propel the device. We then review various other microrobot technologies that have been developed including actuator design and fabrication, power and control electronics design, programming via a finite state machine, and the development of bioinspired fiber arrays. These technologies were then successfully integrated into the device. The robot is now functioning and we have already fabricated three iterations of the proposed device. We hope with further design iterations to produce a fully operational model in the near future

Piezoelectric actuators are advantageous for microrobots due to their light weight, high bandwidth, high force production, low power consumption, and simplicity of integration. However, the main disadvantage of either stack or cantilever piezoelectric actuators are the high drive voltages required for adequate force and displacement. This especially limits the ability for such actuators to be used in autonomous microrobots because of the weight and complexity of necessary power electronics. This paper approaches the design of all the component parts of an autonomous piezoelectric robot as a linear constraint on the weight and efficiency of those components. It then focuses on the choice and optimization of the power electronics section of the robot, specifically exploring three different high voltage generation methods. Finally, one of these power electronics designs is implemented and its behavior is experimentally explored

Mechanisms utilizing rigid links and relatively small flexural joints are very suitable for fabrication at the meso scale. The Micromechanical Flying Insect (MFI) project at UC Berkeley has developed a simple fabrication method which works very well at the scale where the links are a few millimeters in length and the flexures are few hundred microns in length. Previous analysis has concentrated on the geometry of the composite material links for creating rigid links. Recently, we have found that for useful performance, detailed analysis is required of the flexures also. This paper presents a brief analysis of the issues involved in the design of the flexural components of such mechanisms.

We are developing a process to quickly prototype millirobotic systems in which the approach is to identify and develop a construction kit for fabricating almost any design, similar to the kits that are available for larger-scale robots. Two of the basic elements of the kit, the links and flexure joints, have been identified, and an assembly method has been developed. This paper deals with the problem of integrating the wiring in these parts, a significant task on this size scale. This novel feature is achieved through the use of a flexible ribbon cable consisting of three wires made out of patterned copper foil and polyimide. Low melting point solder has been tested successfully to make the electrical interconnect between the parts. We discuss the issues that must be addressed in designing the flexure-wiring combination. In addition, the paper presents the methodology for fabricating structures with integrated wiring using a simple four bar mechanism as an example. Finally, the tests show that the wiring loop over a flexure connecting a distally located sensor on the mechanism maintains both its electrical and mechanical integrity even during large motions. Future work will include the automated assembly of the parts with a low cost assembly tool.

In the following work, we develop a characterization method using miniature fiberoptic position sensors for the Micromechanical Flying Insect (MFI) 1, a centimeter sized micro aerial vehicle being developed at the University of California, Berkeley. Sensing the state of a structure of this scale is challenging due to limited sensor technology and difficulty in constraining the structure. We developed a unique fiberoptic reflection position sensor and associated circuitry that yields a high resolution (approximately 5 µ m of linear motion), appropriate scale, and real time method for sensing the state of the MFI. Also included is the development of a clamping technique for the 2 wing, 4 degree of freedom MFI designed to expose actuator surfaces to be sensed while properly grounding the MFI without introducing added compliance or stiffness to the airframe. We include characterization data for a 2 DOF (flapping and rotation for one wing) wing structure, a clamped 4 DOF motor core of the MFI, and one side of an entire 4 DOF MFI.

To keep pace with recent advances in micro robotic structures demands actuator technologies which can deliver high power and precise motion. For electroactive material based actuators, high power typically implies either high field or high current drives which may lead to greater nonlinearities such as saturation, softening, and increased loss. Physical modeling of actuators is normally taken to be linear since the range of displacements, applied loads, and applied fields is typically small. If extrapolated to high drive conditions, these linear models significantly over predict the power which can be delivered. For actuators driving dynamic systems, a complete nonlinear model of the system will improve controllability and give more accurate estimations of power delivery capabilities. Here static nonlinearities and dynamic linear and nonlinear parameters are derived for high performance piezoelectric bending actuators.

This paper presents the fabrication and the testing of piezoelectric unimorph actuators with embedded piezoelectric sensors which are meant to be used for the actuation of the Micromechanical Flying Insect (MFI). First the fabrication process of a piezoelectric bending actuator comprising a standard unimorph and a rigid extension is described together with the advantages of adding such an extension. Then the convenience of obtaining an embedded piezoelectric sensor by a simple and inexpensive variation of the fabrication process is pointed out. A model for the sensor embedded into a unimorph actuator with rigid extension is derived together with its flat response band limits. Calibration steps are also outlined which allow, despite residual parasitic actuator-sensor coupling, the use of the actuator with the embedded sensor for measuring position and inertial forces when external mechanical structures are driven. An experiment is carried out which validates the model for the actuator/sensor device under desired operating conditions. Preliminary application of the fabricated device to the MFI is also presented where the mechanical power fed into the wing is estimated.

This paper proposes techniques to fabricate synthetic gecko foot-hairs for future wall-climbing robots, and models for understanding the synthetic hair design issues. Two nanomolding fabrication techniques are proposed: the first method uses nanoprobe indented flat wax surface and the second one uses a nano-pore membrane as a template. These templates are molded with silicone rubber, polyimide, etc. type of polymer under vacuum. Next, design parameters such as length, diameter, stiffness, density, and orientation of hairs are determined for non matting and rough surface adaptability. Preliminary nano-hair prototypes showed adhesion close to the predicted values for natural specimens.

The use of high performance composite materials provides a substantial performance improvement for microrobotics. Such materials have great benefits over common MEMs materials such as better fracture toughness and fatigue properties than semiconductors, and higher stiffness to weight ratios than most metals. Composite structures yield remarkable improvements in microrobotic links and joints, as well as greater performance actuators while allowing complicated microrobotic mechanisms to be easily rapid prototyped. The use of such materials in the construction of the 4DOF, 26 joint Micromechanical Flying Insect has reduced the thorax inertia by a factor of 3 and given a 20% increase in resonant frequency over previous designs while cutting construction time from weeks to days.

Four prototypes of biomimetic sensors have been designed and implemented for flight control of a robotic flying insect. The ocelli use four photodiodes to detect changes in light intensity in the surrounding. The halteres use piezo-actuated vibrating structures to sense body rotational velocities via the Coriolis forces. The optic flow sensors consist of linear arrays of elementary motion detectors (EMDs) to register optic flows. The magnetic field sensor uses three metal loops to detect changes in the magnetic field. Despite simplicity and novelty, the preliminary tests on these devices showed promising performance for using such biomimetic sensors on a robotic flying insect.

This paper presents some recent improvements in the fabrication and control of the micromechanical flying insect (MFI), a centimeter sized aerial vehicle currently being developed at the University of California, Berkeley. We report a lift of 506 /spl mu/N from a single wing, which is sufficient for a 100 mg machine to lift itself off the ground. This lift matches very well with predictions based on quasi steady state models. We present some recent improvements in thorax fabrication leading to the development of a light weight platform (/spl sim/ 100 mg), which generates 400 /spl mu/N of lift with a single wing. We also present a new sensor mechanism, which makes it possible to sense the motion of the actuators without having to add anything to the structure itself.

We have developed new methods for the automated assembly of prototype structures and we illustrate them with the construction of a simple one DOF 5mm surgical wrist employing polyester flexures instead of revolute joints. The first step in the structural assembly involves the construction of hollow stainless steel triangular beams that are used for the rigid elements of the structure. It includes the development of a folding fixture to bend stainless steel sheets and the determination of a folding angle sequence by static analysis using a compliant mechanism model. The semi-automatic process of using a millirobot (orthotweezers) to manipulate and assemble the beams and attach the flexures is described in detail. The paper ends with a description of the procedure used to design the wrist.

The first force map has been generated for a 2 DOF wing designed for the MFI project. For the wing beating at a resonance frequency of 139 Hz, the average 3-D forces were found as a function of sinusoidal voltage amplitude and actuator phase difference. An image sequence of the wing trajectory allowed comparison to simulated forces using a quasi-steady state aerodynamic approximation. Finally, the results were compared to the case of ideally matched leading/lagging wing dynamics driven by sinusoids.

This paper presents an analysis of the major mechanical component (the thorax) of the micromechanical flying insect (MFI), a centimeter sized aerial vehicle currently in development at UC Berkeley. We present a description of the kinematics of the mechanism which converts piezoelectric actuation into complex 3D wing motion. A complete non-linear modeling of the system based on the Lagrangian energy technique is presented. A design methodology is presented in order to achieve optimal matching conditions. Two kinds of sensors which are presently utilized on the MFI are described. Experimental results are presented which validate some of the modeled non-linear aspects of the mechanism.

Orienting parts that measure only a few micrometers in diameter introduces several challenges that need not be considered at the macro-scale. First, there are several kinds of sticking effects due to Van der Waals forces and static electricity which complicate hand-off motions and release of a part. Second, the degrees of freedom of micromanipulators are limited. The paper proposes a pair of manipulation primitives and a complete algorithm that addresses these challenges. We show that a sequence of these two manipulation primitives can uniquely orient any asymmetric part while maintaining contact without sensing. This allows us to apply the same plan to many (identical) parts simultaneously. For asymmetric parts we can find a plan of length O(n) in O(n) time that orients the part, where n is the number of vertices.

The mechanism which-real flying insects use to detect body rotation has been simulated. The results show that an angular rate sensor can be made based on such a biological mechanism. Two types of biomimetic gyroscopes have been constructed using foils of stainless steel. The first device is connected directly to a compliant cantilever. The second device is placed on a mechanically amplifying fourbar structure. Both devices are driven by piezoelectric actuators and detect the Coriolis force using strain gages. The experimental results show successful measurements of angular velocities and these devices have the benefits of low power and high sensitivity.

This paper focuses on the design, fabrication and characterization of unimorph actuators for a microaerial flapping mechanism. PZT-SH and PZN-PT are investigated as piezoelectric layers in the unimorph actuators. Design issues for microaerial flapping actuators are discussed, and criteria for the optimal dimensions of actuators are determined. For low power consumption actuation, a square wave based electronic driving circuit is proposed. Fabricated piezoelectric unimorphs are characterized by an optical measurement system in quasi-static and dynamic mode. Experimental performance of PZT-5H and PZIV-PT based unimorphs is compared with desired design specifications. A 1-DOF flapping mechanism with a PZT-SH unimorph is constructed, and 180/spl deg/ stroke motion at 95 Hz is achieved. Thus, it is shown that unimorphs could be promising flapping mechanism actuators.

Considers a 2 DOF resonant thorax structure signed and fabricated for the MFI project. Miniature piezoelectric PZN-PT unimorph actuators were fabricated and used to drive a four-bar transmission mechanism. The current thorax design utilizes two actuated four-bars and a spherical joint to drive a rigid wing. Rotationally compliant flexure joints have been tested with lifetimes over 10/sup 6/ cycles. Wing spars were instrumented with strain gauges for force measurement and closed-loop wing control.

We describe a microassembly system based on two one degree of freedom probes ("ortho-tweezers") and a three degree of freedom translating stage, controlled by a Java application with Python scripting support. We describe how basic manipulation primitives can be combined in a Python script to perform automated, force-feedback controlled assembly operations. We demonstrate a fully automated pick and place task using 200/spl times/200/spl times/100 micron blocks. Using a temporary handling block, the system can manipulate long, thin, fragile parts, such as semiconductor strain gauges.

Key to the success of the micromechanical flying insect (MFI) project is the development sensors for flight force measurement. At the lowest level of MFI control is the wing control system which relies on wing and thorax mounted force sensors. These sensors have a dual function of stroke by stroke force characterization and system identification as well as the use in feedback control for all levels. There are two methods for force sensing on a flying robotic insect: measurements directly on the thorax, and body force measurement with a trade-off in design between sensor bandwidth and sensitivity.

Flapping wings provide unmatched manoeuvrability for flying microrobots. Recent advances in modelling insect aerodynamics show that adequate wing rotation at the end of the stroke is essential for generating adequate flight forces. We developed a thorax structure using four bar frames combined with an extensible fan-fold wing to provide adequate wing stroke and rotation. Flow measurements on a scale model of the beating wing show promising aerodynamics. Calculations using a simple resonant mechanical circuit model show that piezoelectric actuators can generate sufficient power, force and stroke to drive the wings at 150 Hz.

In this paper, we quantify several spatial capabilities of the human tactile system needed for tactile feedback, or teletaction. Psychophysics experiments measure the amplitude resolution of the human tactile system, the effects of shear stress on grating orientation discrimination, and the effects of viscoelasticity (creep and relaxation) on tactile perception for static touch. The results are used to determine teletaction system design parameters. We find that 10% amplitude resolution is sufficient for a teletaction system with a 2 mm elastic layer and 2 mm tactor spacing.

A teletaction system uses a tactile display to present the user with information about texture, local shape, and/or local compliance. Current tactile displays are flat and rigid, and require precise machining and assembly of many parts. This paper describes the fabrication and performance of a one-piece pneumatically-actuated tactile display molded from silicone rubber. Tactor spacing is 2.5 mm with 1 mm diameter tactor elements. Tactile display compliance ensures contact between the finger and tactile display at all times. Unlike previous pneumatic tactile displays, there is no chamber leakage and no seal friction. A psychophysics experiment showed that a synthetic grating on the tactile display was perceived as well as a low-pass-filtered real contact.

The Acrobot is a simple underactuated system consisting of a double pendulum with an actuator at the second joint only. We derive a set of exact trajectories of the nonlinear equations of motion, which involve inverted periodic motions. The trajectories can be made arbitrarily fast by an appropriate choice of the Acrobot mass and length parameters. Next, we present a nonlinear control law and show how it can be applied to the Acrobot to track these trajectories. In simulations we compare tracking results for our controller and one based on pseudo-linearization. The pseudo-linearizing controller produces significant error for a 1 Hz trajectory, while ours produces none. Finally, we present experimental results which demonstrate that the assumptions of the theory were not overly restrictive. In particular, peak-to-peak oscillations of joints as large as 850 were obtained, despite real-world effects, such as joint friction, inexact parameter values, and noisy and delayed joint velocity data.

An example of a planar hopping robot is considered, which has only one actuated joint. Simulations demonstrate that the robot can perform both sliding and hopping gaits, despite the fact that almost all other hopping robots have at least two actuated joints.

Teletaction is the transmission of cutaneous information from a remote tactile sensor to an operator's skin, typically the finger tips. Ideally, one would like a realistic sensation of directly touching an object with one's own finger and sense properties such as local shape, hardness, or texture. Teletaction or tactile feedback is one component of haptic feedback, the other component being force or kinesthetic feedback. This paper considers design issues for teletaction systems, particularly sampling density, aliasing, and the limitations of using an array of 1-DOF actuators to approximate a continuous stress distribution on the human finger.

This paper discusses the design and testing of an eight-by-eight tactile capacitive array sensor for detection of sub-millimeter features and objects, where the entire sensor array is smaller than normal human spatial resolution of 1 mm. Each square taction is less than 100 /spl mu/m on a side, with similar spacing between elements. The structural material was doped polysilicon with an air gap dielectric of 0.5 /spl mu/m. A thin (50-80 /spl mu/m) protective layer of silicone rubber was adhered to the polysilicon surface of the sensor to provide interpolation of normal loads between elements. The sensors were tested and possessed good spatial uniformity, the capability of detecting millinewton forces, and good interpolation between elements. The sensors had severe hysteresis problems, but no detectable proximity effects.

This papers analyzes the reliability of radius of curvature estimates from tactile sensor data. A linear elastic model is used to fit the indenter parameters, load, location, and curvature, to the sensor output. It was found that both contact models and calibration techniques could dramatically effect the bias and variance of the estimated indenter parameters. The Fourier series is found to be an appropriate basis in which to analyze both the calibration of tactile sensors and the problem of band limited shape interpretation.

When parts to be handled are less than one millimeter in size, adhesive forces between gripper and object can be significant compared to gravitational forces. These adhesive forces arise primarily from surface tension, Van der Waals, and electrostatic attractions and can be a fundamental limitation to part handling in a gas environment. While it is possible to fabricate miniature versions of conventional robot grippers, for example from polysilicon, it appears that it will be difficult to overcome adhesion effects for the smallest parts. Thus, manipulation of parts on the order of 10 micron or smaller may best be done in a fluid medium using techniques such as laser trapping, or dielectrophoresis.

Underactuated mechanisms provide significant challenges to the control engineer. In this paper a nonlinear tracking controller is applied to the underactuated Acrobot, a double pendulum with an actuator at only the second joint. Tracking of oscillatory trajectories with joint angle magnitude up to 85/spl deg/ was achieved. Applications to one-legged robot locomotion are described.>

A linear elastic plane strain model for a cylindrical finger with a solid core and elastic surface is developed. This model is used to determine the subsurface strain impulse responses as well as pressure distributions in the contact region for indentation of the cylinder by rigid objects with friction. Singular value decomposition is used to find a reduced basis in which to analyze the shape-from-strain inversion problem. This decomposition shows that sensor depth must be small to achieve good shape sensing. However, if only contact location and applied force magnitude and direction are required, deep sensors can quickly and easily provide this information.

Dextrous robot hands need to be able to determine the pose of objects to reliably grasp and manipulate them. The first contacts with an object can be used to provide an initial estimate of this information if the object is constrained to be of a particular class. The authors consider a simple example of exploiting class constraints: finding the axis of an unknown surface of revolution. Three tactile curvature measurements on a surface of revolution with twice-differentiable sweeping rule function are shown to be sufficient for determining the axis except for certain singular configurations. Position and orientation error uncertainties and experimental results are presented for a cylindrical tactile sensor.>

A new example of a hopping robot is considered, consisting simply of two links (the end of one link acts as the foot) joined by an actuated, revolute joint. For the stance phase a nonlinear controller is derived that maintains the balance of the robot and periodically accelerates the center of mass vertically. For large enough oscillations the robot can slide or take off. If flight is achieved, the drift caused by non-zero angular momentum can typically be cancelled by rotating the actuated joint an integral number of times, and the robot can land in the same configuration in which it took off. This is due to the holonomy of a single rotation of the actuated joint. Results of simulations are presented in which the robot achieves both sliding and hopping gaits.>

A dynamic simulation of threaded insertion is developed based on Euler's equations, impulsive forces, and a geometric description for threaded parts. Points of contact between the threaded parts are determined and tracked during the simulation. Reaction forces are computed based by the kinematic description. The simulation is used to investigate the behavior of a bolt during insertion into a nut under grasp stiffness and damper control.>

It is shown how contact curvature can be determined from a single contact with a cylindrical tactile sensor. When the tactile finger touches an unknown smooth convex surface, contact location, principal curvatures, and normal force are determined from a 4*4 window of strain measurements. Contact properties are determined by a nonlinear model-based inversion from strain measurements back to the contact type. Sensor strains are predicted by convolving the spatial impulse response of the rubber skin with the assumed surface pressure distribution derived from a Hertz contact model. Gradient search finds the parameters of the convex second-order shape and the force that best fit the sensor data. Experiments under laboratory conditions show radius estimation within 10%, orientation within 3%, and subtactel (tactile element) localization to 3% of the element spacing. Using a linearized model, error bounds due to sensor noise on the inversion process are predicted.>

Sparse tactile sensing can be used to determine the positions and orientations of objects if the objects are restricted to being of a particular class. Consideration is given to a simple example of exploiting class constraints: finding the axis of an unknown surface of revolution. Three tactile curvature measurements on a surface of revolution with sweeping rule in C/sup 2/ are shown to be sufficient for determining the axis except for certain singular configurations. Position and orientation error bounds and preliminary experimental results are presented for a capacitive tactile sensor with two contacts. Optimal angular spacing was seen to be 90 degrees between contacts. Experiments showed that the method worked with a position error of 0.07 in. and an angle error of 7.3 degrees .>

Tests were performed on a thumb-shaped tactile sensor containing an 8 by 20 array of tactile elements. Each element measures the strain of the rubber finger material at a point below the surface of the finger. To characterize the finger behavior, a precision force application device was designed. Static tests determined the steady-state linearity of the elements with respect to force magnitude. The frequency response was determined in the range of 0.10 to 20 Hz. Permanent deformation due to stress was seen to be predictable. The Maxwell-Kelvin model for viscoelasticity was fit to the stress-strain data obtained by probing the finger and recording the applied force and the strain response of a single element. Results showed it to be better than a spring model. A second-order model was also fit to the stress-strain data. The model was inverted to predict the magnitude of the force of a point contact given the strain of one tactile element. The inverse model predicted the fore better than the spring model.>

A force strategy developed by R.S. Fearing (1986) for automatically grasping two-dimensional polygon objects by a dextrous hand with point contact with friction is shown to be applicable to three-dimensional polyhedral objects. The algorithm essentially consists of position control of one finger and force control of the other along the internal force directions. Basic geometric constraints on the object are obtained for feasible grasping with two fingers. It is observed that, when an object is rotated about the line passing through soft finger contacts, the fingers slip on the object in a simple predictable trajectory.>

A description is given of a device for determining curvatures using a cylindrical tactile sensor. The finger touches an unknown convex surface. Principal curvatures, normal force and location are determined from a 4*4 window of strain measurements. Sensor strains are predicted by convolving the spatial impulse response of the rubber skin with the assumed surface pressure distribution derived from a Hertz contact model. Gradient search finds the parameters of the convex second-order shape and the force that best fit the sensor data. Experiments show radius estimation within 10%, orientation within 2.5 degrees, and sub-tactel localization of 3% of the element spacing. Accuracy limits due to sensor noise are derived.>

A tactile sensing finger tip for the Stanford/JPL Hand has been developed. This sensor incorporates an 8 × 8 sensor array with complete coverage of the cylindrical finger tip. A preliminary analysis has been done to determine contact center, magnitude, and orientation, and to judge if the constructed sensor has adequate sensitivity and density. This low level tactile information provides the first steps needed for reliable object manipulation in a dextrous hand. Experiments were performed during an open loop re-grasping manipulation to determine how well the sensors and algorithms performed.

The robotics group of the Stanford Artificial Intelligence Laboratory is currently developing a new computational system for robotics applications. Stanford's NYMPH system uses multiple NSC 32016 processors and one MC68010 based processor, sharing a common Intel Multibus. The 32K processors provide the raw computational power needed for advanced robotics applications, and the 68K provides a pleasant interface with the rest of the world. Software has been developed to provide useful communications and synchronization primitives, without consuming excessive processor resources or bus bandwidth. NYMPH provides both large amounts of computing power and a good programming environment, making it an effective research tool.

This paper describes a method to reorient grasped rigid objects of polygonal cross-section using open loop force control strategies. A representation of forces in a spherical reference frame has been developed that ensures grasp stability and allows simple commands to control object reorientation. A procedure is shown for controlling at which fingers slip or rotation occurs, that can be used for three orthogonal rotations of an object grasped with three fingers. The implementation of a "twirling rotation" on the Stanford/JPL hand is described. A failure analysis is presented for potential causes for the object to slip from the grasp. Object control strategies are developed assuming line contacts and infinitesimal finger sizes. The influence of cylindrical finger tips on the performance of reorientations is described.

A method is presented for stably grasping two dimensional polygonal objects with a dextrous hand when object models are not available. Basic constraints on object vertex angles are found for feasible grasping with two fingers. Local tactile information can be used to determine the finger motion that will reach feasible grasping locations. With an appropriate choice of finger stiffnesses, a hand can automatically grasp these objects with two fingers. The bounded slip of a part in a hand is shown to be valuable for adapting the fingers and object to a stable situation. Examples are given to show the ability of this grasping method to accommodate disturbance forces and to perform simple part reorientations and regrasping operations.

In order to stably grasp objects without using object models, tactile feedback from the fingers is sometimes necessary. This feedback can be used to adjust grasping forces to prevent a part from slipping from a hand. If the angle of force at the object finger contact can be determined, slip can be prevented by the proper adjustment of finger forces. Another important tactile sensing task is finding the edges and corners of an object, since they are usually feasible grasping locations. This paper describes how this information can be extracted from the finger-object contact using strain sensors beneath a compliant skin. For determining contact forces, strain measurements are easier to use than the surface deformation profile. The finger is modelled as an infinite linear elastic half plane to predict the measured strain for several contact types and forces. The number of sensors required is less than has been proposed for other tactile recognition tasks. A rough upper bound on sensor density requirements for a specific depth is presented that is based on the frequency response of the elastic medium. The effects of different sensor stiffnesses on sensor performance are discussed.