We present a robotic table tennis platform that achieves a variety of hit styles and ball-spins with high precision, power, and consistency. This is enabled by a custom lightweight, high-torque, low rotor inertia, five degree-of-freedom arm capable of high acceleration. To generate swing trajectories, we formulate an optimal control problem (OCP) that constrains the state of the paddle at the time of the strike. The terminal position is given by a predicted ball trajectory, and the terminal orientation and velocity of the paddle are chosen to match various possible styles of hits: loops (topspin), drives (flat), and chops (backspin). Finally, we construct a fixed-horizon model predictive controller (MPC) around this OCP to allow the hardware to quickly react to changes in the predicted ball trajectory. We validate on hardware that the system is capable of hitting balls with an average exit velocity of$11 \mathrm{m} / \mathrm{s}$at an 88% success rate across the three swing types.

We revisit the concept of constraint embedding as a means for dealing with kinematic loop constraints during dynamics computations for rigid-body systems. Specifically, we consider the local loop constraints emerging from common actuation sub-mechanisms in modern robotics systems (e.g., geared motors, differential drives, and four-bar mechanisms). As a complementary perspective to prior work on constraint embedding, we present an analysis that generalizes the traditional concepts of joint models and motion/force subspaces between individual rigid bodies to generalized joint models and motion/force subspaces between groups of rigid bodies subject to loop constraints. We then use these generalized concepts to derive the constraint-embedded recursive forward dynamics algorithm using multi-handle articulated bodies. We demonstrate the broad applicability of the generalized joint concepts by showing how they also lead to the constraint-embedding-based recursive algorithm for inverse dynamics. Lastly, we benchmark our open-source implementation in C++ for the forward dynamics algorithm against state-of-the-art, sparsity-exploiting algorithms. Our alternative derivation is intended to make the constraint embedding methodology more accessible to the broader robotics community, while the benchmarking study clarifies the relative strengths and limitations of constraint embedding versus sparsity-exploiting methods. Indeed, our benchmarking validates that constraint embedding outperforms the non-recursive alternative in cases involving local kinematic loops.

Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

We present a minimal phase oscillator model for learning quadrupedal locomotion. Each of the four oscillators is coupled only to itself and its corresponding leg through local feedback of the ground reaction force, which can be interpreted as an observer feedback gain. We interpret the oscillator itself as a latent contact state-estimator. Through a systematic ablation study, we show that the combination of phase observations, simple phase-based rewards, and the local feedback dynamics induces policies that exhibit emergent gait preferences, while using a reduced set of simple rewards, and without prescribing a specific gait. The code is open-source, and a video synopsis available at https://youtu.be/1NKQ0rSV3jU.

In this work, we introduce a control framework that combines model-based footstep planning with Reinforcement Learning (RL), leveraging desired footstep patterns derived from the Linear Inverted Pendulum (LIP) dynamics. Utilizing the LIP model, our method forward predicts robot states and determines the desired foot placement given the velocity commands. We then train an RL policy to track the foot placements without following the full reference motions derived from the LIP model. This partial guidance from the physics model allows the RL policy to integrate the predictive capabilities of the physics-informed dynamics and the adaptability characteristics of the RL controller without overfitting the policy to the template model. Our approach is validated on the MIT Humanoid, demonstrating that our policy can achieve stable yet dynamic locomotion for walking and turning. We further validate the adaptability and generalizability of our policy by extending the locomotion task to unseen, uneven terrain. During the hardware deployment, we have achieved forward walking speeds of up to 1.5 m/s on a treadmill and have successfully performed dynamic locomotion maneuvers such as 90-degree and 180-degree turns.

We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of constrained optimization problems rather than a sequence of nonlinear systems of equations. The insight behind our proposed algorithm is formulating the discovery of this sequence of optimization problems as a search problem in a multidimensional homotopy parameter space. Our proposed algorithm, the Probabilistic Homotopy Optimization algorithm, switches between solve and sample phases, using solutions to easy problems as initial guesses to more challenging problems. We analyze how our algorithm performs in the presence of common challenges to homotopy methods, such as bifurcation, folding, and disconnectedness of the homotopy solution manifold. Finally, we demonstrate its utility via a case study on two dynamic motion planning problems. the cart-pole and the MIT Humanoid.

The main challenge in developing effective reinforcement learning (RL) pipelines is often the design and tuning the reward functions. Well-designed shaping reward can lead to significantly faster learning. Naively formulated rewards, however, can conflict with the desired behavior and result in overfitting or even erratic performance if not properly tuned. In theory, the broad class of potential based reward shaping (PBRS) can help guide the learning process without affecting the optimal policy. Although several studies have explored the use of potential based reward shaping to accelerate learning convergence, most have been limited to grid-worlds and low-dimensional systems, and RL in robotics has predominantly relied on standard forms of reward shaping. In this paper, we benchmark standard forms of shaping with PBRS for a humanoid robot. We find that in this high-dimensional system, PBRS has only marginal benefits in convergence speed. However, the PBRS reward terms are significantly more robust to scaling than typical reward shaping approaches, and thus easier to tune.

Model predictive control (MPC) is a powerful tool to control systems with non-linear dynamics and constraints, but its computational demands impose limitations on the dynamics model used for planning. Instead of using a single complex model along the MPC horizon, model hierarchy predictive control (MHPC) reduces solve times by planning over a sequence of models of varying complexity within a single horizon. Choosing this model sequence can become intractable when considering all possible combinations of reduced order models and prediction horizons. We propose a framework to systematically optimize a model schedule for MHPC. We leverage trajectory optimization (TO) to approximate the accumulated cost of the closed-loop controller. We trade off performance and solve times by minimizing the number of decision variables of the MHPC problem along the horizon while keeping the approximate closed-loop cost near optimal. The framework is validated in simulation with a planar humanoid robot as a proof of concept. We find that the approximated closed-loop cost matches the simulated one for most of the model schedules, and show that the proposed approach finds optimal model schedules that transfer directly to simulation, and with total horizons that vary between 1.1 and 1.6 walking steps.

Modern robotic manipulation systems fall short of human manipulation skills partly because they rely on closing feedback loops exclusively around vision data, which reduces system bandwidth and speed. By developing autonomous grasping reflexes that rely on high-bandwidth force, contact, and proximity data, the overall system speed and robustness can be increased while reducing reliance on vision data. We are developing a new system built around a low-inertia, high-speed arm with nimble fingers that combines a high-level trajectory planner operating at less than 1 Hz with low-level autonomous reflex controllers running upwards of 300 Hz. We characterize the reflex system by comparing the volume of the set of successful grasps for a naive baseline controller and variations of our reflexive grasping controller, finding that our controller expands the set of successful grasps by 55% relative to the baseline. We also deploy our reflexive grasping controller with a simple vision-based planner in an autonomous clutter clearing task, achieving a grasp success rate above 90% while clearing over 100 items.

We introduce a spherical fingertip sensor for dynamic manipulation. It is based on barometric pressure and time-of-flight proximity sensors and is low-latency, compact, and physically robust. The sensor uses a trained neural network to estimate the contact location and three-axis contact forces based on data from the pressure sensors, which are embedded within the sensor's sphere of polyurethane rubber. The time-of-flight sensors face in three different outward directions, and an integrated microcontroller samples each of the individual sensors at up to 200 Hz. To quantify the effect of system latency on dynamic manipulation performance, we develop and analyze a metric called the collision impulse ratio and characterize the end-to-end latency of our new sensor. We also present experimental demonstrations with the sensor, including measuring contact transitions, performing coarse mapping, maintaining a contact force with a moving object, and reacting to avoid collisions.

Dynamic jumping with legged robots poses a challenging problem in planning and control. Formulating the jump optimization to allow fast online execution is difficult; efficiently using this capability to generate long-horizon motion plans further complicates the problem. In this work, we present a hierarchical planning framework to address this problem. We first formulate a real-time tractable trajectory optimization for performing omnidirectional jumping. We then embed the results of this optimization into a low dimensional jump feasibility classifier. This classifier is leveraged to produce geometric motion plans that select dynamically feasible jumps while mitigating the effects of the process noise. We deploy our framework on the Mini Cheetah Vision quadruped, demonstrating the robot's ability to generate and execute reliable, goal-oriented plans that involve forward, lateral, and rotational jumps onto surfaces as tall as the robot's nominal hip height. The ability to plan through omnidirectional jumping greatly expands the robot's mobility relative to planners that restrict jumping to the sagittal or frontal planes.

Quadrupedal landing is a complex process involving large impacts, elaborate contact transitions, and is a crucial recovery behavior observed in many biological animals. This work presents a real-time, optimal landing controller that is free of pre-specified contact schedules. The controller determines optimal touchdown postures and reaction force profiles and is able to recover from a variety of falling configurations. The quadrupedal platform used, the MIT Mini Cheetah, recovered safely from drops of up to 8 m in simulation, as well as from a range of orientations and planar velocities. The controller is also tested on hardware, successfully recovering from drops of up to 2 m.

Humans noticeably swing their arms for balancing and locomotion. Although the underlying biomechanical mechanisms have been studied, it is unclear how robots can fully take advantage of these appendages. Most controllers that exploit arms for balance and locomotion rely on feedback and cannot anticipate incoming disturbances and future states. Model predictive controllers readily address these drawbacks but are computationally expensive. Here, we leverage recent work on model hierarchy predictive control (MHPC). We develop an MHPC formulation that plans arm motions in reaction to expected or unexpected disturbances. We tested multiple model compositions using simulated balance experiments with the MIT Humanoid undergoing various disturbances. We found that an MHPC formulation that plans over a full-body kino-dynamic model for a 0.3 s horizon followed by a single rigid body model for 0.5 s horizon runs at 40 Hz and increases the set of disturbances that the robot can withstand. Arms allow the robot to dissipate momentum quickly and move the center of mass independently from the lower body. This kinematic advantage helps generate ground wrenches while avoiding kinematic singularities and keeping the center of mass and center pressure within the support polygon. We note similar advantages when allowing the MHPC to anticipate incoming disturbances.

We present a proprioceptive teleoperation system that uses a reflexive grasping algorithm to enhance the speed and robustness of pick-and-place tasks. The system consists of two manipulators that use quasi-direct-drive actuation to provide highly transparent force feedback. The end-effector has bimodal force sensors that measure 3-axis force information and 2-dimensional contact location. This information is used for anti-slip and re-grasping reflexes. When the user makes contact with the desired object, the re-grasping reflex aligns the gripper fingers with antipodal points on the object to maximize the grasp stability. The reflex takes only 150ms to correct for inaccurate grasps chosen by the user, so the user's motion is only minimally disturbed by the execution of the re-grasp. Once antipodal contact is established, the anti-slip reflex ensures that the gripper applies enough normal force to prevent the object from slipping out of the grasp. The combination of proprioceptive manipulators and reflexive grasping allows the user to complete teleoperated tasks with precision at high speed.

This work presents a two part framework for online planning and execution of dynamic aerial motions on a quadruped robot. Motions are planned via a centroidal momentum-based nonlinear optimization that is general enough to produce rich sets of novel dynamic motions based solely on the user-specified contact schedule and desired launch velocity of the robot. Since this nonlinear optimization is not tractable for real-time receding horizon control, motions are planned once via nonlinear optimization in preparation of an aerial motion and then tracked continuously using a variational-based optimal controller that offers robustness to the uncertainties that exist in the real hardware such as modeling error or disturbances. Motion planning typically takes between 0.05-0.15 s, while the optimal controller finds stabilizing feedback inputs at 500 Hz. Experimental results on the MIT Mini Cheetah demonstrate that the framework can reliably produce successful aerial motions such as jumps onto and off of platforms, spins, flips, barrel rolls, and running jumps over obstacles.

Optimization based predictive control is a powerful tool that has improved the ability of legged robots to execute dynamic maneuvers and traverse increasingly difficult terrains. However, it is often challenging and unintuitive to design meaningful cost functions and build high-fidelity models while adhering to timing restrictions. A novel framework to extract and design principled regularization heuristics for legged locomotion optimization control is presented. By allowing a simulation to fully explore the cost space offline, certain states and actions can be constrained or isolated. Data is fit with simple models relating the desired commands, optimal control actions, and robot states to identify new heuristic candidates. Basic parameter learning and adaptation laws are then applied to the models online. This method extracts simple, but powerful heuristics that can approximate complex dynamics and account for errors stemming from model simplifications and parameter uncertainty without the loss of physical intuition while generalizing the parameter tuning process. Results on the Mini Cheetah robot verify the increased capabilities due to the newly extracted heuristics without any modification to the controller structure or gains.

Legged robots have been highlighted as promising mobile platforms for disaster response and rescue scenarios because of their rough terrain locomotion capability. In cluttered environments, small robots are desirable as they can maneuver through small gaps, narrow paths, or tunnels. However small robots have their own set of difficulties such as limited space for sensors, limited obstacle clearance, and scaled-down walking speed. In this paper, we extensively address these difficulties via effective sensor integration and exploitation of dynamic locomotion and jumping. We integrate two Intel RealSense sensors into the MIT Mini-Cheetah, a 0.3 m tall, 9 kg quadruped robot. Simple and effective filtering and evaluation algorithms are used for foothold adjustment and obstacle avoidance. We showcase the exploration of highly irregular terrain using dynamic trotting and jumping with the small-scale, fully sensorized Mini-Cheetah quadruped robot.

Animal-level agility and robustness in robots cannot be accomplished by solely relying on blind locomotion controllers. A significant portion of a robot's ability to traverse terrain comes from reacting to the external world through visual sensing. However, embedding the sensors and compute that provide sufficient accuracy at high speeds is challenging, especially if the robot has significant space limitations. In this paper, we propose a system integration of a small-scale quadruped robot, the MIT Mini-Cheetah Vision, that exteroceptively senses the terrain and dynamically explores the world around it at high velocities. Through extensive hardware and software development, we demonstrate a fully untethered robot with all hardware onboard running a locomotion controller that combines state-of-the-art Regularized Predictive Control (RPC) with Whole-Body Impulse Control (WBIC). We devise a hierarchical state estimator that integrates kinematic, IMU, and localization sensor data to provide state estimates specific to path planning and locomotion tasks. Our integrated system has demonstrated robust autonomous waypoint tracking in dynamic real-world environments at speeds of over 1 m/s with high rates of success.

The ability to measure multi-axis contact forces and contact surface normals in real time is critical to allow robots to improve their dexterous manipulation and locomotion abilities. This paper presents a new fingertip sensor for 3-axis contact force and contact location detection, as well as improvements on an existing footpad sensor through use of a new artificial neural network estimator. The fingertip sensor is intended for use in manipulation, while the footpad sensor is intended for high force use in locomotion. Both sensors consist of pressure sensing elements embedded within a rubber hemisphere, and utilize an artificial neural network to estimate the applied forces (fx, fy, and fz), and contact angles (θ and φ) from the individual sensor element readings. The sensors are inherently robust, and the hemispherical shape allows for easy integration into point feet and fingertips. Both the fingertip and footpad sensors demonstrate the ability to track forces and angles accurately over the surface of the hemisphere (θ=±45° and φ=±45°) and can experience up to 25N and 450N normal force, respectively, without saturating. The performance of the sensor is demonstrated with experimental results of dynamic control of a robotic arm with real-time sensor feedback.

Mini Cheetah is a small and inexpensive, yet powerful and mechanically robust quadruped robot, intended to enable rapid development of control systems for legged robots. The robot uses custom backdriveable modular actuators, which enable high-bandwidth force control, high force density, and robustness to impacts. Standing around 0.3 m tall and weighing 9 kg, Mini Cheetah can easily be handled by a single operator. We have demonstrated dynamic trot, trot-run, bounding, and pronking gaits on the robot to speeds of up to 2.45 meters per second using Convex Model-Predictive Control (cMPC). In addition to locomotion, we have used the robot to execute 360° backflips, with trajectories generated using offline nonlinear optimization.

This paper presents a novel methodology for implementing optimized jumping behavior on quadruped robots. Our method includes efficient trajectory optimization, precise high-frequency tracking controller and robust landing controller for stabilizing the robot body position and orientation after impact. Experimental validation was successfully conducted on the MIT Cheetah 3, enabling the robot to repeatably jump onto and jump down from a desk with the height of 30" (0.76 m). The result demonstrates the advantages of the approach as well as the capability of the robot hardware itself.

This work presents a successful implementation of a nonlinear optimization-based Regularized Predictive Control (RPC) for legged locomotion on the MIT Cheetah 3 robot platform. Footstep placements and ground reaction forces at the contact feet are simultaneously solved for over a prediction horizon in real-time. Often in academic literature not enough attention is given to the implementation details that make the theory work in practice and many times it is precisely these details that end up being critical to the success or failure of the theory in real world applications. Nonlinear optimization for real-time legged locomotion control in particular is one of the techniques that has shown promise, but falls short when implemented on hardware systems subjected to computation limits and undesirable local minima. We discuss various algorithms and techniques developed to overcome some of the challenges faced when implementing nonlinear optimization-based controllers for dynamic legged locomotion.

In robotic tasks that require physical interactions such as manipulation and legged locomotion, it is important to simultaneously measure contact forces and contact angles. This paper presents a unified solution for simultaneously measuring three axis contact forces and contact angles for legged locomotion or manipulation. Unlike most tactile sensors, the presented design utilizes the stress field method by sampling pressures over multiple locations within an elastomer, enabling inherently robust operation against impact and abrasive interactions. The presented sensor is designed for point-feet quadrupedal robots and can be easily scaled down for other applications such as grasping. The sampled stress distribution is mapped to output forces fx, fy, and fzand two contact angles, θ and ψ on the hemispherical sensor surface via Gaussian process regression. The prototype sensor is able track normal and shear forces accurately, achieving a normalized root mean (RMS) squared error of only 1.00% - 1.36% for fzacross multiple tests with up to 180N normal force, and a normalized RMS error of 1.71% - 4.67% and 1.82% - 6.68% for fxand fy, respectively, with up to 80N shear force. Additionally, the footpad is able to estimate the contact location coordinates θ and ψ with a normalized RMS error of 2.69% -7.51% over a range of 0-40° and 2.79% - 9.62% over a range of 0-30°, respectively. The footpad can estimate contact location over a maximum range of θ = ±45° and ψ = ±45°, and can withstand over 450N of normal force at location θ = ψ = 0° without reaching saturation. This prototype demonstrates the ability to simultaneously measure force in three axes and contact angles using Gaussian process regression, with the potential to explore other regression methods for embedded computing and miniaturization of the design for finger tip scale sensors.

As legged robots are sent into unstructured environments, the ability to robustly manage contact transitions will be a critical skill. This paper introduces an approach to probabilistically fuse contact models, managing uncertainty in terrain geometry, dynamic modeling, and kinematics to improve the robustness of contact initiation at touchdown. A discrete-time extension of the generalized-momentum disturbance observer is presented to increase the accuracy of proprioceptive force control estimates. This information is fused with other contact priors under a framework of Kalman Filtering to increase robustness of the method. This approach results in accurate contact detection with 99.3 % accuracy and a small 4-5ms delay. Using this new detector, an Event-Based Finite State Machine is implemented to deal with unexpected early and late contacts. This allows the robot to traverse cluttered environments by modifying the control actions for each individual leg based on the estimated contact state rather than adhering to a rigid time schedule regardless of actual contact state. Experiments with the MIT Cheetah 3 robot show the success of both the detection algorithm, as well as the Event-Based FSM while making unexpected contacts during trotting.

This paper exemplifies the design process for legged machines capable of dynamic behaviors. In order to achieve high performance robots, it is crucial to guarantee harmonious integration between software and hardware. Hence, the development of such capable robotic platforms must address design requirements that meet the assumptions of typical model-based controllers but also respect the physical limitations of a real system. First, we show that proper hardware design choices can greatly aid the control algorithm by approximating the physical robot to the template assumptions. We include actuation and sensing design examples that allows a simple model to capture a major portion of the natural dynamic behavior of the physical machine. Results are applied to a real robot (Figure 1) and we show that the adopted methodology is able to address typical problems in legged robots such as high bandwidth force control and robustness to impact. Finally, a simple model-based balance controller that takes advantage of the fidelity of the template model to the real machine is implemented. These are examples of software-hardware codesign processes that vastly facilitate robotic control.

This paper introduces a new robust, dynamic quadruped, the MIT Cheetah 3. Like its predecessor, the Cheetah 3 exploits tailored mechanical design to enable simple control strategies for dynamic locomotion and features high-bandwidth proprioceptive actuators to manage physical interaction with the environment. A new leg design is presented that includes proprioceptive actuation on the abduction/adduction degrees of freedom in addition to an expanded range of motion on the hips and knees. To make full use of these new capabilities, general balance and locomotion controllers for Cheetah 3 are presented. These controllers are embedded into a modular control architecture that allows the robot to handle unexpected terrain disturbances through reactive gait modification and without the need for external sensors or prior environment knowledge. The efficiency of the robot is demonstrated by a low Cost of Transport (CoT) over multiple gaits at moderate speeds, with the lowest CoT of 0.45 found during trotting. Experiments showcase the ability to blindly climb up stairs as a result of the full system integration. These results collectively represent a promising step toward a platform capable of generalized dynamic legged locomotion.

This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20-30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.

This paper presents a method to achieve human and legged robot dynamic synchronization through bilateral feedback teleoperation. Our study shows how we can explore the interplay between human Extrapolated Center of Mass and the contact forces with the environment in order to transmit to the robot the underlying balancing and stepping strategy. All the necessary key equations for the frontal plane coupled dynamics are presented along with the human feedback law derived from the proposed state normalization in length and time. Here, we pay special attention to how the natural frequency of each system influences the resulting motion and analyze how the coupled system responds to various robot sizes. Experiments in which a human operator controls a simulated bipedal robot show how the Balance Feedback Interface force varies according to different scales and responds to external disturbances. Finally, we show the method's robustness to uneven terrain and how we can allow the point feet robot to synchronously take steps with the operator. This is an introductory study that aims to grant legged robots motor capabilities for power manipulation comparable to humans.

This paper presents the ongoing work towards enabling robots to achieve highly dynamic behavior through full-body teleoperation. Human operator and robot slave have independent balance controllers that interact with each other during the experiments. First we present a compliant balancing controller that regulates the feet contact forces in order to mitigate external disturbances and maintain balance. Next, by estimating the forces that the operator exerts over its own Center of Mass to generate movement, the Dynamic Synchronization Force Scaling controller allows the robot to anticipate human motion during posture tracking. This strategy requires reduced control gains for state tracking when compared to purely reactive controllers, resulting in an inherently more stable system. Results show a considerable reduction of the position tracking overshoot along with substantial reduction of required error-based control forces.

This paper describes additive self-folding, an origami-inspired rapid fabrication approach for creating actuatable compliant structures. Recent work in 3-D printing and other rapid fabrication processes have mostly focused on rigid objects or objects that can achieve small deformations. In contrast, soft robots often require elastic materials and large amounts of movement. Additive self-folding is a process that involves cutting slices of a 3-D object in a long strip and then pleat folding them into a likeness of the original model. The zigzag pattern for folding enables large bending movements that can be actuated and controlled. Gaps between slices in the folded model can be designed to provide larger deformations or higher shape accuracy. We advance existing planar fabrication and self-folding techniques to automate the fabrication process, enabling highly compliant structures with complex 3-D geometries to be designed and fabricated within a few hours. We describe this process in this paper and provide algorithms for converting 3-D meshes into additive self-folding designs. The designs can be rapidly instrumented for global control using magnetic fields or tendon-driven for local bending. We also describe how the resulting structures can be modeled and their responses to tendon-driven control predicted. We test our design and fabrication methods on three models (a bunny, a tuna fish, and a starfish) and demonstrate the method's potential for actuation by actuating the tuna fish and starfish models using tendons and magnetic control.

This paper introduces a new policy-regularized model-predictive control (PR-MPC) approach to automatically generate and stabilize a diverse set of quadrupedal gaits. Model-predictive methods offer great promise to address balance in dynamic robots, yet require the solution of challenging nonlinear optimization problems when applied to legged systems. The new proposed PR-MPC approach aims to improve the conditioning of these problems by adding regularization based on heuristic reference policies. With this approach, a unified MPC formulation is shown to generate and stabilize trotting, bounding, and galloping without retuning any cost-function parameters. Intuitively, the added regularization biases the solution of the MPC towards common heuristics from the literature that are based on simple physics. Simulation results show that PR-MPC improves the computation time and closed-loop outcomes of applying MPC to stabilize quadrupedal gaits.

Designing an actuator system for highly dynamic legged robots has been one of the grand challenges in robotics research. Conventional actuators for manufacturing applications have difficulty satisfying design requirements for high-speed locomotion, such as the need for high torque density and the ability to manage dynamic physical interactions. To address this challenge, this paper suggests a proprioceptive actuation paradigm that enables highly dynamic performance in legged machines. Proprioceptive actuation uses collocated force control at the joints to effectively control contact interactions at the feet under dynamic conditions. Modal analysis of a reduced leg model and dimensional analysis of DC motors address the main principles for implementation of this paradigm. In the realm of legged machines, this paradigm provides a unique combination of high torque density, high-bandwidth force control, and the ability to mitigate impacts through backdrivability. We introduce a new metric named the “impact mitigation factor” (IMF) to quantify backdrivability at impact, which enables design comparison across a wide class of robots. The MIT Cheetah leg is presented, and is shown to have an IMF that is comparable to other quadrupeds with series springs to handle impact. The design enables the Cheetah to control contact forces during dynamic bounding, with contact times down to 85 ms and peak forces over 450 N. The unique capabilities of the MIT Cheetah, achieving impact-robust force-controlled operation in high-speed three-dimensional running and jumping, suggest wider implementation of this holistic actuation approach.

We present a new teleoperated micromanipulation system in which all units of the system, wearable user interface devices and a slave micromanipulator, are manufactured by engraving, cutting, and folding two-dimensional materials. The designed manipulation system employs a simple hydraulic mechanism consisting of pairs of syringes that have different diameters, which allows for motion reduction and physical interaction between the master and the slave. As a result, users can precisely manipulate micro-objects without tremor, which was previously difficult with bare hands. This paper presents design considerations and features fabrication methods, performance metrics of this creative manipulation system, and a range of high-level micromanipulation abilities such as pick-and-place, microseparation, and three-dimensional microassembly. Highlighting rapid design and fabrication of a low-cost precision micromanipulation system, this paper proposes new applications of folded machines to wearable robots and microrobotics.

Dynamic behavior of legged robots is strongly affected by ground impedance. Empirical observation of robot hardware is needed because ground impedance and foot-ground interaction is challenging to predict in simulation. This paper presents experimental data of the MIT Super Mini Cheetah robot hopping on hard and soft ground. We show that controllers tuned for each surface perform better for each specific surface type, assessing performance using measurements of 1.) stability of the robot in response to self-disturbances applied by the robot onto itself and 2.) the peak accelerations of the robot that occur during ground impact, which should be minimized to reduce mechanical stress. To aid in controller selection on different ground types, we show that the robot can measure ground stiffness and friction in-situ by measuring its own interaction with the ground. To motivate future work in variable-terrain control and in-situ ground measurement, we show preliminary results of running gaits that transition between hard and soft ground.

This paper presents a new approach to the characterization of tactile array sensors that aims to reduce the computational time needed for convergence to obtain a useful estimator for normal and shear forces. This is achieved by breaking up the sensor characterization into two parts: a linear regression portion using multivariate least squares regression, and a nonlinear regression portion using a neural network as a multi-input, multi-output function approximator. This procedure has been termed Least Squares Artificial Neural Network (LSANN). By applying LSANN on the 2nd generation MIT Cheetah footpad, the convergence speed for the estimator of the normal and shear forces is improved by 59.2% compared to using only the neural network alone. The normalized root mean squared error between the two methods are nearly identical at 1.17% in the normal direction, and 8.30% and 10.14% in the shear directions. This approach could have broader implications in greatly reducing the amount of time needed to train a contact force estimator for a large number of tactile sensor arrays (i.e. in robotic hands and skin).

This paper presents the ongoing work towards enabling humanoid robots to achieve dynamic behaviors comparable to humans. By using the concept of Divergent Component of Motion (DCM) first in introduced in [1], the present paper permits operator and robot balance synchronization using the mutual dynamics of the Center of Mass (CoM) and Center of Pressure (CoP). The Linear Inverted Pendulum Model (LIPM) with a reaction mass [2] is utilized to capture the humanoid behavior which interacts with the human operator under the Equilibrium Point (EP) [3] control assumption. Remarkable similarities between the physical system behavior and simulated results suggest the feasibility of the strategy. Experiments conducted with the MIT HERMES humanoid robot further show the performance of the proposed method.

This paper introduces a bounding gait control algorithm that allows a variable-speed running in the MIT Cheetah 2. A simple impulse planning algorithm is proposed to design vertical and horizontal force profiles which make net impulse on the system during one cycle zero. This design of force profiles leads to the conservation of linear momentum over a complete step, providing periodicity in horizontal and vertical velocity. When designed profiles are applied to the system, periodic orbits with an ability to change running speed are obtained. A virtual compliance control in the horizontal and vertical direction has been added onto the designed force profiles to stabilize the periodic orbits. The experimental results show that the algorithm successfully achieved untethered 3D running of the MIT Cheetah 2, with speeds ranging from 0 m/sec to 4.5 m/sec on treadmills as well as on grassy fields.

Computational thinking is an important part of a modern education, and robotics provides a powerful tool for teaching programming logic in an interactive and engaging way. The robot garden presented in this paper is a distributed multi-robot system capable of running autonomously or under user control from a simple graphical interface. Over 100 origami flowers are actuated with LEDs and printed pouch motors, and are deployed in a modular array around additional swimming and crawling folded robots. The garden integrates state-of-the-art rapid design and fabrication technologies with distributed systems software techniques to create a scalable swarm in which robots can be controlled individually or as a group. The garden can be used to teach basic algorithmic concepts through its distributed algorithm demonstration capabilities and can teach programming concepts through its education-oriented user interface.

Self-assembling robots can be transported and deployed inexpensively and autonomously in remote and dangerous environments. In this paper, we introduce a novel self-assembling method with a planar pneumatic system. Inflation of pouches translate into shape changes, turning a sheet of composite material into a complex robotic structure. This new method enables a flat origami-based robotic structure to self-fold to desired angles with pressure control. It allows a static joint to become dynamic, self-actuate to reconfigure itself after initial folding. Finally, the folded robot can unfold itself at the end of a robotic application. We believe this new pneumatic approach provides an important toolkit to build more powerful and capable self-assembling robots.

This paper introduces the phenomenon of directional efficiency, a property of spur gear transmissions in which the coefficient of torque dependent efficiency is function of the power flow direction; the efficiency in the step-up direction differs from that of step-down. Understanding the directional efficiency is important in robot design where the mechanical impedance of the transmission significantly affects the dynamics of physical interaction with the environment. This paper is the first to address `backdrivability' by investigating directional efficiency on a high gear ratio robotic actuator, industrial servo gearboxes and over a family of gears. The kinematic model shows that a single pair of gears operates at higher efficiency in step-down than in step-up and the effect is confirmed in experiment, albeit with discrepancy in the magnitude of difference. Experimental results show that step-down and step-up directional efficiency are 98% and 96% respectively for a PIC DESIGNS 6:1 gearbox over the range of tested velocities. Additionally the overall energy efficiencies of the Dynamixel robotic servo motor with a gear ratio of 248:1 are approximately 75% and 70% for step-down and step-up respectively over a range of tested velocities. For the Dynamixel servo actuator, modeling with directional efficiency coefficients reduces error in predicted output force to 2-4% compared to a 4-8% with a single efficiency coefficient and 30% for models without friction.

Origami-engineering is an emerging design and manufacturing technology for creating 3-D robotic systems using 2-D designs. We present a new origami-inspired tele-micromanipulation system manufactured by printing and folding. The developed micromanipulation system consists of two miniature machines, wearable user interface devices and a multi degree-of-freedom slave manipulator. A simple hydraulic system using syringes allows motion reduction and force transmission between the master and the slave. This paper introduces how to design and rapidly prototype these devices, and, finally, demonstrate different micromanipulation abilities such as 2-D trajectory following, pick-and-place, and 3-D micro-assembly. Highlighting rapid design and fabrication of a low-cost high performance origami-based tele-micromanipulation system, this paper proposes new applications of origami-inspired printable robots to wearable robots, micro-robotics and tele-operation.

This paper introduces a novel Balance Feedback Interface (BFI) that addresses the problem of bilateral feedback for teleoperation of humanoid robots. With this new device we expect to enhance robot's high force manipulation performance to a level comparable to humans by dynamically synchronizing master and slave. Through this Human-Machine Interface (HMI) we aim to achieve two goals: (i) have the human pilot learn from the robot's dynamic behavior; and (ii) have the humanoid robotic platform learn from human's motor skills. The eventual goal is to fuse the teleoperator's commands and an autonomous controller for optimal performance. Initial results evaluate the stability of the robot while being teleoperated by a human pilot for a simple upright balancing task. During the experiment the user has no visual information about the robot's state and is expected to compensate for unpredicted instabilities. The bilateral feedback system shows robustness to inertial variations and to external disturbances with the proposed human-in-the-loop control strategy offering valuable insight for future work.

Self-folding is a promising technique for assembling robots from flat sheets. However, existing implementations do not include reliable methods for sensing the folding angle, making feedback control impossible. In this paper, we present novel angle sensors for foldable robots and machines. They are inkjet printed and fully integrated into robots' laminate. This additional sensor layer tracks the angle motion of robot hinges, to better guide robot assembling by folding and to perform more complicated tasks that requires feedback control, making folded robots more capable in real world applications. We introduce the fabrication process, property assessments, and demonstrate sensor performance by measuring folding angles of a cube and controlling folds on a gripper.

We propose soft planar actuators enhanced by free-form fabrication that are suitable for making everyday objects move. The actuator consists of one or more inflatable pouches with an adhesive back. We have developed a machine for the fabrication of free-from pouches; squares, circles and ribbons are all possible. The deformation of the pouches can provide linear, rotational, and more complicated motion corresponding to the pouch's geometry. We also provide a both manual and programmable control system. In a user study, we organized a hands-on workshop of actuated origami for children. The results show that the combination of the actuator and classic materials can enhance rapid prototyping of animated objects.

We propose a new family of fluidic soft actuators called Pouch Motors. The pouch motors are developed to create printable actuators for enhancing mass-fabrication of robots from sheet materials using easily accessible tools. The pouch motor consists of one or more gas-tight bladders (called pouches) fabricated by heat bonding. We developed two types of actuators from inflatable pouches: the linear pouch motor and the rotational pouch motor. Our theoretical analysis predicts the static force-length and moment-angle relationships of these actuators under pressure control. We compare the theoretical bounds with actual results achieved using several fabricated devices. We developed a fabrication process of pouch motors using a heat stamping technique that allows mass-manufacturing. We also demonstrate three robot bodies with embedded pouch motors: a parallel gripper, a robotic arm with antagonistic actuation, and legged walking robot with a self-contained miniature pneumatic system.

This paper presents a control system platform architecture developed for multi-degrees of freedom (DoFs) robots capable of highly dynamic movements. In robotic applications that require rapid physical interactions with the environment, it is critical for the robot to achieve a high frequency synchronization of data processing from a large number of high-bandwidth actuators and sensors. To address this important problem in robotics, we developed a control system architecture that effectively utilizes the advantages of modern parallel real-time computing technologies: multicore CPU, the Field Programmable Gate Array (FPGA), and distributed local processors. This approach was implemented in the fast running experiments of the MIT Cheetah. In such a highly dynamic robot, the required control bandwidth is particularly high since the MIT Cheetah's leg actuation system is designed to generate high force (output torque up to 100Nm) with high bandwidth (400Hz electrical, 120Hz mechanical) with minimal mechanical impedance for fast locomotive capability. On the integrated control system, a multi-layered architecture is programmed. Inspired by the MapReduce model and the pipelining method, more than 50 processes are operated in parallel, and major processes among them are optimized to achieve the maximum throughput. The proposed architecture enables the control update frequency 4 kHz. With this control system platform, we achieved a high-force proprioceptive impedance control [1], and a trot-running up to 6 m/s with a locomotion efficiency rivaling animals [2]. This control system architecture is well suited for the future trend towards real-time computing system and, thus can be a candidate for a future standard robot control platform.

Numerous legged robots have demonstrated the effectiveness of tuned leg impedance to achieve dynamically stable running and hopping. However, selecting appropriate impedance values for new machines remains challenging. This paper investigates the effect of joint impedance selection on locomotion stability and efficiency by analyzing a simulation model of the MIT Cheetah quadruped robot performing a trot gait. An exhaustive search of impedance parameters of the knee and hip shows that locomotion stability is highly sensitive to knee impedance and insensitive to hip impedance. Inspection of simulations operating during a ground-height disturbance reveals why: During a disturbance response most of the variation in work performed in the legs occurs in the knee joints. Mechanical work data from the MIT Cheetah exhibits close experimental agreement with the simulation predictions. The exhaustive search also reveals that, within the range of impedance parameters that can achieve stable locomotion, joint impedance values do not have a significant effect on the mechanical cost of transport. These results indicate that the dynamic response of the leg-extension degree of freedom is of primary importance to achieving dynamically stable running, and that robust stability may be achieved with minimal compromise of locomotion efficiency.

The MIT Cheetah demonstrated a stable 6 m/s trot gait in the sagittal plane utilizing the self-stable characteristics of locomotion. This paper presents a numerical analysis of the behavior of a quadruped robot model with the proposed controller. We first demonstrate the existence of periodic trot gaits at various speeds and examine local orbital stability of each trajectory using Poincar`e map analysis. Beyond the local stability, we additionally demonstrate the stability of the model against large initial perturbations. Stability of trot gaits at a wide range of speed enables gradual acceleration demonstrated in this paper and a real machine. This simulation study also suggests the upper limit of the command speed that ensures stable steady-state running. As we increase the command speed, we observe series of period-doubling bifurcations, which suggests presence of chaotic dynamics beyond a certain level of command speed. Extension of this simulation analysis will provide useful guidelines for searching control parameters to further improve the system performance.

This paper introduces a bounding gait control algorithm that allows a successful implementation of duty cycle modulation in the MIT Cheetah 2. Instead of controlling leg stiffness to emulate a ‘springy leg’ inspired from the Spring-Loaded-Inverted-Pendulum (SLIP) model, the algorithm prescribes vertical impulse by generating scaled ground reaction forces at each step to achieve the desired stance and total stride duration. Therefore, we can control the duty cycle: the percentage of the stance phase over the entire cycle. By prescribing the required vertical impulse of the ground reaction force at each step, the algorithm can adapt to variable duty cycles attributed to variations in running speed. Following linear momentum conservation law, in order to achieve a limit-cycle gait, the sum of all vertical ground reaction forces must match vertical momentum created by gravity during a cycle. In addition, we added a virtual compliance control in the vertical direction to enhance stability. The stiffness of the virtual compliance is selected based on the eigenvalue analysis of the linearized Poincaré map and the chosen stiffness is 700 N/m, which corresponds to around 12% of the stiffness used in the previous trotting experiments of the MIT Cheetah, where the ground reaction forces are purely caused by the impedance controller with equilibrium point trajectories. This indicates that the virtual compliance control does not significantly contributes to generating ground reaction forces, but to stability. The experimental results show that the algorithm successfully prescribes the duty cycle for stable bounding gaits. This new approach can shed a light on variable speed running control algorithm.

In robotic single-port surgery, it is desirable for a manipulator to exhibit the property of variable stiffness. Small-port incisions may require both high flexibility of the manipulator for safety purposes, as well as high structural stiffness for operational precision and high payload capability. This paper presents a new hyperredundant tubular manipulator with a variable neutral-line mechanisms and adjustable stiffness. A unique asymmetric arrangement of the tendons and the links realizes both articulation of the manipulator and continuous stiffness modulation. This asymmetric motion of the manipulator is compensated by a novel actuation mechanism without affecting its structural stiffness. The paper describes the basic mechanics of the variable neutral-line manipulator, and its stiffness characteristics. Simulation and experimental results verify the performance of the proposed mechanism.

In this paper, we introduce the design principles for highly efficient legged robots and the implementation of the principles on the MIT Cheetah robot. Three major energy loss modes during locomotion are heat losses through the actuators, losses through the transmission, and the interaction losses that includes all losses of the system interacting with the environment. We propose four design principles that minimize these losses: employment of high torque density motors, low impedance transmission, energy regenerative electronics and a design architecture that minimizes the leg inertia. We present the design features of the MIT cheetah robot as an embodiment of these principles. The resulting cost of transport (COT) is 0.51 during 2.3 m/s running, which rivals running animals in the same scale.

This paper presents a novel “layer jamming” mechanism that can achieve variable stiffness. The layer jamming mechanism exploits the friction present between layers of thin material, which can be controlled by a confining pressure. Due to the mechanism's hollow geometry, compact size, and light weight, it is well suited for various minimally invasive surgery applications, where stiffness change is required. This paper describes the concept, the mathematical model, and a tubular snake-like manipulator prototype. Various characteristics of layer jamming, such as stiffness and yield strength, are studied both theoretically and experimentally.

This paper presents a novel design approach for a two-DOF foot force sensor for a high speed running quadruped. The adopted approach harnesses the deformation property of an elastomeric material to relate applied force to measurable deformation. A lightweight, robust and compact magnetic-field based sensing system, consisting of an assembly of miniature hall-effect sensors, is employed to infer the positional information of a magnet embedded in the elastomeric material. Instead of solving two non-linear models (magnetic field and elastomeric) sequentially, a direct approach of using artificial neural networks (ANN) is utilized to relate magnetic flux density (MFD) measurements to applied forces. The force sensor, which weighs only 24.5 gms, provides a measurement range of 0 – 1000 N normal to the ground and up to ± 125N parallel to the ground. The mean force measurement accuracy was found to be within 7% of the applied forces. The sensor designed as part of this work finds direct applications in ground reaction force sensing for a running quadrupedal robot.

This paper presents Optimally Scaled Hip-Force Planning (OSHP), a novel approach to controlling the body dynamics of running robots. Controllers based on OSHP form the high-level component of a hierarchical control scheme in which they direct lower level controllers, each responsible for coordinating the motion of a single leg. An OSHP controller takes in the state of the runner at the apex of its primary aerial phase and returns desired profiles for the vertical and horizontal forces to be exerted at each hip during the subsequent stride. The hip force profiles returned by OSHP are scaled variants of nominal force profiles based on biological ground reaction force data. The OSHP controller determines the scaling parameters for these profiles through constrained nonlinear optimization on an approximate model of the runner's body dynamics. Evaluation of an OSHP controller for a quadruped model in simulation shows that even with very simple leg controllers, the OSHP controller can accelerate the runner from rest to steady-state running without a pre-defined footfall sequence.

Animals use tails to improve locomotion performance; here we assess how the biomimetic MIT Cheetah robot can do the same. Analysis proves that for a given power and weight, tails can provide greater average torque than reaction wheels for the short times of interest in high speed running. A simple tail controller enables the cheetah to perform aerial orientation maneuvers in simulation. The MIT Cheetah robot's tail rejects an impulsive disturbance from a `wrecking ball' in experiments. This study demonstrates that a tail will help the MIT Cheetah achieve its goal of 30mph locomotion by 2014.

This paper illustrates the fabrication and characterization of a footpad based on an original principle of volumetric displacement sensing. It is intended for use in detecting ground contact forces in a running quadrupedal robot. The footpad is manufactured as a monolithic, composite structure composed of multi-graded polymers which are reinforced by glass fiber to increase durability and traction. The volumetric displacement sensing principle utilizes a hyperelastic gel-like pad with embedded magnets that are tracked with Hall-effect sensors. Normal and shear forces can be detected as contact with the ground which causes the gel-like pad to deform into rigid wells. This is all done without the need to expose the sensor. A one-time training process using an artificial neural network was used to relate the normal and shear forces with the volumetric displacement sensor output. The sensor was shown to predict normal forces in the Z-axis up to 80N with a root mean squared error of 6.04% as well as the onset of shear in the X and Y-axis. This demonstrates a proof-of-concept for a more robust footpad sensor suitable for use in all outdoor conditions.

Legged locomotion involves periodic negative and positive work, which usually results in high power consumption. Improvement of the energy efficiency is possible by using energy storage elements to reversibly store the negative work performed during a walking or running cycle. While series elastics with high impedance (high gear ratio) actuators are widely used, we investigate the application of parallel stiffness with highly backdriveable actuators. We specifically show that the use of parallel springs in a bounding quadruped with a flexible spine can lower power consumption by over 50%.

This paper introduces a new mechanism for achieving tunable stiffness, named layer jamming, and presents a hollow snake-like manipulator having tunable stiffness capability. The layer jamming mechanism is composed of multiple layers of thin Mylar film, and makes use of amplified friction between the films by applying vacuum pressure. In contrast to other tunable stiffness technology, such as particle jamming or field-activated materials (MR or ER fluids), layer jamming occupies a small volume and thus can be applied to small, light weight manipulators. The snake-like manipulator presented here is composed only of Mylar film and wires, and has highly flexible and under-actuated properties without application of a vacuum; however, it becomes highly stiff when a vacuum is applied. In this paper the characteristics of layer jamming are explored: its stiffness and breaking strength are obtained both theoretically and experimentally, and a prototype manipulator is developed and experimentally characterized.

High speed legged locomotion involves high acceleration and extensive loadings of the leg, which impose critical challenges in actuator design. We introduce actuator dimensional analysis for maximizing torque density and transmission `transparency'. A front leg prototype developed based on insight from the analysis is evaluated for direct proprioceptive force control without force sensors. The vertical stiffness controlled leg was tested on a material testing device to calibrate the mechanical impedance of the leg. By compensating transmission impedance from commanded torque, the leg was able to estimate impact force. For the impact test, the mean absolute error as a ratio of full scale sensor force is 0.041 in the 3406 N/m stiffness experiment and is 0.049 in the 5038 N/m experiment. The results indicate that prescribed force profile control is possible during high speed locomotion.

Swing-leg retraction was introduced as a way to improve the stability and disturbance rejection of running robots. It was also suggested that the reduced foot speed due to swing-leg retraction can help reduce impact energy losses, decrease peak forces, and minimize foot slipping. However, the extent to which swing-leg retraction rate influences all these benefits was unknown. In this paper, we present a study on the effect of swing-leg retraction rate on these benefits. The results of this study show that swing-leg retraction can indeed improve the performance of running robots in all of the suggested areas. However, the results also show that, for moderate and high running speeds, the optimal retraction rate for maximal disturbance rejection and stability is different from the optimal retraction rate for minimal impact losses, peak forces, and foot slipping. This discrepancy indicates an inherent tradeoff to consider when selecting the retraction rate for a robot control system: in general, retraction rate can be optimized for better stability and disturbance rejection or for more favorable efficiency, impact forces, and footing stability, but not all simultaneously. Furthermore, this tradeoff becomes more severe as running speed increases.

Swing leg retraction reduces touchdown energy losses of running by decreasing foot speed at the moment of ground contact, but does the additional acceleration of the swing leg cost more energy than is saved? To determine whether swing leg retraction can increase the overall energy efficiency of running robots, we find the optimally efficient gaits of a McGeer-like runner over a range of retraction rates. Results show that overall energy usage, including that used to swing the legs, scales with energy loss at touchdown, which is minimized at the retraction rate that zeros foot tangential speed at ground contact. Other benefits of swing leg retraction, such as reduced foot slippage and damaging touchdown forces, are realized simultaneously with optimal energy efficiency.

This paper presents a soft robotic platform that exhibits peristaltic locomotion. The design principle is based on the unique antagonistic arrangement of radial/circular and longitudinal muscle groups of Oligochaeta. Sequential antagonistic motion is achieved in a flexible braided mesh-tube structure with NiTi coil actuators. A numerical model for the mesh structure describes how peristaltic motion induces robust locomotion and details the deformation by the contraction of NiTi actuators. Several peristaltic locomotion modes are modeled, tested, and compared on the basis of locomotion speed. The entire mechanical structure is made of flexible mesh materials and can withstand significant external impacts during locomotion. This approach can enable a completely soft robotic platform by employing a flexible control unit and energy sources.

For a new class of soft robotic platforms, development of flexible and robust actuators is quintessential. Remarkable resilience, shape memory effect, high energy density, and scalability are attributed to nickel titanium (NiTi) making it an excellent actuator candidate for meso-scale applications. This paper presents a micro-muscle fiber crafted from shape memory alloy (NiTi) coiled springs. An enhanced spring NiTi model describes the combination of martensite deformation and spring effect due to its geometry. This paper also describes a manufacturing process and characterization for micro-scale NiTi coil actuators in various annealing temperatures. The presented fiber is 400µm in diameter and 0.5m in length exhibiting 50% contraction and 1226J/kg of energy density with 40g of force. By changing the geometry of the spring, force-displacement characteristics can be tuned. An enhanced-performance inverted-spring manufacturing method is also described and characterized. A method of discrete displacement control is presented. Taking advantage of the flexibility of micro-coil spring, we present a novel mesh-worm prototype that utilizes bio-inspired antagonistic actuation for its body deformation and locomotion.

The adhesive and frictional properties of dry adhesive materials can be described by a three-dimensional limit surface in the space of normal and tangential contact forces at the feet. We present the empirically derived limit surface for directional adhesive pads and illustrate its application to controlling the forces at the feet of a robot climbing on arbitrary slopes, including overhanging surfaces. For the directional adhesive patches that we have developed, the limit surface is convex, which permits efficient computation of the desired internal and external forces among the feet to maximize a safety margin with respect to disturbance forces on the robot. The limit surface also intersects the origin in force space, which enables efficient climbing without wasting energy in attaching and detaching the feet. These insights are applied to an experimental climbing platform demonstrating the proper use of directional adhesion and mimicking the climbing behavior seen in geckos.

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We describe the design and control of a new bio-inspired climbing robot designed to scale smooth vertical surfaces using directional adhesive materials. The robot, called Stickybot, draws its inspiration from geckos and other climbing lizards and employs similar compliance and force control strategies to climb smooth vertical surfaces including glass, tile and plastic panels. Foremost among the design features are multiple levels of compliance, at length scales ranging from centimeters to micrometers, to allow the robot to conform to surfaces and maintain large real areas of contact so that adhesive forces can support it. Structures within the feet ensure even stress distributions over each toe and facilitate engagement and disengagement of the adhesive materials. A force control strategy works in conjunction with the directional adhesive materials to obtain sufficient levels of friction and adhesion for climbing with low attachment and detachment forces.

Recent biological research suggests that reliable, agile climbing on smooth vertical surfaces requires controllable adhesion. In nature, geckos control adhesion by properly loading the compliant adhesive structures on their toes. These strongly anisotropic dry adhesive structures produce large frictional and adhesive forces when subjected to certain force/motion trajectories. Smooth detachment is obtained by simply reversing these trajectories. Each toe's hierarchical structure facilitates intimate conformation to the climbing surface resulting in a balanced stress distribution across the entire adhesive area. By controlling the internal forces among feet, the gecko can achieve the loading conditions necessary to generate the desired amount of adhesion. The same principles have been applied to the design and manufacture of feet for a climbing robot. The manufacturing process of these Directional Polymer Stalks is detailed along with test results comparing them to conventional adhesives.