Legged robot locomotion is hindered by a mismatch between applications where legs can outperform wheels or treads, most of which feature deformable substrates, and existing tools for planning and control, most of which assume flat, rigid substrates. In this study, we focus on the ramifications of plastic terrain deformation on the hop-to-hop energy dynamics of a spring-legged monopedal hopping robot animated by a switched-compliance energy injection controller. From this deliberately simple robot-terrain template, we derive a hop-to-hop energy return map, and we use physical experiments and simulations to validate the hop-to-hop energy map for a real robot hopping on a real deformable substrate. The dynamical properties (fixed points, eigenvalues, basins of attraction) of this map provide insights into efficient, responsive, and robust locomotion on deformable terrain. Specifically, we identify constant-fixed-point surfaces in a controller parameter space that suggest it is possible to tune control parameters for efficiency or responsiveness while targeting a desired gait energy level. We also identify conditions under which fixed points of the energy map are globally stable, and we further characterize the basins of attraction of fixed points when these conditions are not satisfied. We conclude by discussing the implications of this hop-to-hop energy map for planning, control, and estimation for efficient, agile, and robust legged locomotion on deformable terrain.

Sit-to-Stand (StS) is a fundamental daily activity that can be challenging for stroke survivors due to strength, motor control, and proprioception deficits in their lower limbs. Existing therapies involve repetitive StS exercises, but these can be physically demanding for therapists while assistive devices may limit patient participation and hinder motor learning. To address these challenges, this work proposes the use of two lower-limb exoskeletons to mediate physical interaction between therapists and patients during a StS rehabilitative task. This approach offers several advantages, including improved therapist-patient interaction, safety enforcement, and performance quantification. The whole body control of the two exoskeletons transmits online feedback between the two users, but at the same time assists in movement and ensures balance, and thus helping subjects with greater difficulty. In this study we present the architecture of the framework, presenting and discussing some technical choices made in the design.

Controlling the interaction forces between a human and an exoskeleton is crucial for providing transparency or adjusting assistance or resistance levels. However, it is an open problem to control the interaction forces of lower-limb exoskeletons designed for unrestricted overground walking. For these types of exoskeletons, it is challenging to implement force/torque sensors at every contact between the user and the exoskeleton for direct force measurement. Moreover, it is important to compensate for the exoskeleton's whole-body gravitational and dynamical forces, especially for heavy lower-limb exoskeletons. Previous works either simplified the dynamic model by treating the legs as independent double pendulums, or they did not close the loop with interaction force feedback. The proposed whole-exoskeleton closed-loop compensation (WECC) method calculates the interaction torques during the complete gait cycle by using whole-body dynamics and joint torque measurements on a hip-knee exoskeleton. Furthermore, it uses a constrained optimization scheme to track desired interaction torques in a closed loop while considering physical and safety constraints. We evaluated the haptic transparency and dynamic interaction torque tracking of WECC control on three subjects. We also compared the performance of WECC with a controller based on a simplified dynamic model and a passive version of the exoskeleton. The WECC controller results in a consistently low absolute interaction torque error during the whole gait cycle for both zero and nonzero desired interaction torques. In contrast, the simplified controller yields poor performance in tracking desired interaction torques during the stance phase

In this article, we define “robotic contact juggling” to be the purposeful control of the motion of a 3-D smooth object as it rolls freely on a motion-controlled robot manipulator, or “hand.” While specific examples of robotic contact juggling have been studied before, in this article, we provide the first general formulation and solution method for the case of an arbitrary smooth object in a single-point rolling contact on an arbitrary smooth hand. Our formulation splits the problem into four subproblems: deriving the second-order rolling kinematics; deriving the 3-D rolling dynamics; planning rolling motions that satisfy the rolling dynamics and achieve the desired goal; and stabilization of planned rolling trajectories. The theoretical results are demonstrated in 3-D simulations and 2-D experiments using feedback from a high-speed vision system.

This article describes a topological approach to generating families of open- and closed-loop walking gaits for underactuated 2-D and 3-D biped walkers subject to configuration inequality constraints, physical holonomic constraints (e.g., closed-loop linkages), and virtual holonomic constraints (user-defined constraints enforced through feedback control). Our method constructs implicitly defined manifolds of feasible periodic gaits within a state-time-control space that parameterizes the biped’s hybrid trajectories. Since equilibrium configurations of the biped often belong to such manifolds, we use equilibria as “templates” from which to grow the gait families. Equilibria are reliable seeds for the construction of gait families, eliminating the need for random, intuited, or bio-inspired initial guesses at feasible trajectories in an optimization framework. We demonstrate the approach on several 2-D and 3-D biped walkers.

We introduce a distributed finite element algorithm that allows swarms of mobile robots to persistently monitor environmental quantities such as temperature or salinity. The robots deploy themselves into the environment, covering the domain and dividing it into nonoverlapping regions. Each robot estimates the environment over its own region using local measurements and communication with nearby robots. The algorithm ensures that each robot's estimate constitutes a piece of a global estimate that spans the entire domain, fuses the whole swarm's measurements, and accounts for the spatial correlation between measurement and estimation locations. By incorporating spatial correlation without requiring the transmission of measurements or measurement locations, the algorithm decouples its communication requirements from the spatial statistics of the environment and enables robots with fixed capabilities to monitor environments with different spatial correlation lengths. Analysis and simulation demonstrate that, as the number of robots increases, the memory and communication requirements of each individual robot decrease until reaching a minimum, after which the resolution of the environmental model increases. Additional robots, therefore, add computational resources to the swarm rather than introducing extra computational burdens.

In wireless sensor networks, estimating a global parameter from locally obtained measurements via local interactions is known as the distributed parameter estimation problem. Solving these problems often require the deployment of distributed optimization algorithms that rely on a constant exchange of information among the sensor nodes. This makes such distributed algorithms vulnerable to attackers or malicious nodes that want to gain access to private information regarding the network. Based on the sliding mode control scheme, here we present a novel approach to infer sensitive information (e.g., gradient or private parameters of the local objective function) regarding a node of interest by intercepting the communication between the nodes. The effectiveness of the proposed approach is illustrated in a representative example of distributed event localization using an acoustic sensor network.

In this paper we propose a method for motion planning and feedback control of hybrid, dynamic, and non-prehensile manipulation tasks. We outline five subproblems to address this: determining a set of manipulation primitives, choosing a sequence of tasks, picking transition states, motion planning for each individual primitive, and stabilizing each mode using feedback control. We apply the framework to plan a sequence of motions for manipulating a block with a planar 3R manipulator. We demonstrate preliminary experimental results for a block resting on the manipulator with a desired goal state on a ledge outside of the robot's workspace. The planned primitives reorient the block using a series of fixed, rolling, and sliding contact modes, and throw it to the goal state.

This paper presents a framework for planning the motion of an η -fingered robot hand to create an inertial load on a grasped object to achieve a desired in-grasp sliding motion. The model of the sliding dynamics is based on a soft-finger limit surface contact model at each fingertip. A motion planner is derived to automatically solve for the finger motions for a given initial and desired configuration of the object relative to the fingers. Iterative planning and execution are shown to reduce the errors that occur due to the modeling and trajectory tracking errors. The framework is applied to the problem of regrasping a laminar object held in a pinch grasp. We propose a limited surface model of the contact pressure distribution at each finger to predict the sliding directions. Experimental validations are shown, including iterative error reduction and repeatability of the experiment.

This paper presents a framework for planning the motion of an n-fingered robot hand to create an inertial load on a grasped object to achieve a desired in-grasp sliding motion. The model of the sliding dynamics is based on a soft-finger limit surface contact model at each fingertip. The framework is applied to the problem of regrasping a block held in a pinch grasp. The approach is applied to two examples in simulation, one of which is tested experimentally.

Average consensus estimators enable robots in a communication network to calculate the mean of their local inputs in a distributed manner. Many distributed control methods for robot swarms rely on these estimators. The performance of such estimators depends on their design and the network topology. For mobile sensor networks, this topology may be unknown, making it difficult to design average consensus estimators for optimal performance. We introduce a design method for proportional-integral (PI) average consensus estimators that decouples estimator synthesis from network topology. This method also applies to the more general internal model (IM) estimator, yielding extended PI estimators that improve convergence rates without increasing communication costs. In simulations over many geometric random graphs, the extended PI estimator consistently reduces the estimation error settling time by a factor of five.

In this paper we present a method to stimulate multiple muscles in a human arm to perform interaction tasks, using an implanted Functional Electrical Stimulation (FES) neuroprosthesis. The unstable effect arising from interaction tasks is considered, and the arm stability is directly treated as one of the control objectives in the controller design. By exploiting the kinematic and muscular redundancy of the system, we can control the interaction force and the arm's stiffness property simultaneously, thus ensuring the stable execution of interaction tasks. A representative example of such interaction tasks, namely the “pushing with a stick” task, is simulated. It is found that using our proposed controller, as compared to a previously developed feedforward FES controller that does not consider arm stiffness or stability, the stability of the arm is guaranteed while the task of force control is correctly achieved.

We present a strategy for generating period-one, open-loop walking gaits for multi-degree-of-freedom, planar biped walkers. Our approach uses equilibria of the dynamics as templates, which we connect to a family of period-one walking motions using numerical continuation methods. We define a gait as a fixed point of the walker's hybrid dynamics which resides in a state-time-control space consisting of the robot's post-impact state, switching time (the time at which the swing leg impacts the ground), and a finite set of design or control parameters. We demonstrate our approach on several physically-symmetric biped walkers. In particular, we prove that our approach reduces the search space for an initial gait in the state-time-control space to a one-dimensional search in switching time. We show that we can generates periodic motion without resorting to splines or reference trajectories. Finally, we compare our method to generating gaits with virtual holonomic constraints.

We present a method to experimentally identify the inverse dynamics of a human arm. We drive a person's hand with a robot along smooth reaching trajectories while measuring the motion of the shoulder and elbow joints and the force required to move the hand. We fit a model that predicts the shoulder and elbow joint torques required to achieve a desired arm motion. This torque can be supplied by functional electrical stimulation of muscles to control the arm of a person paralyzed by spinal cord injury. Errors in predictions of the joint torques for a subject without spinal cord injury were less than 20% of the maximum torques observed in the identification experiments. In most cases a semiparametric Gaussian process model predicted joint torques with equal or less error than a nonparametric Gaussian process model or a parametric model.

The ParkourBot climbs in a planar reduced-gravity vertical chute by leaping back and forth between the chute's two parallel walls. The ParkourBot is comprised of a body with two springy legs and its controls consist of leg angles at touchdown and the energy stored in them. During flight, the robot stores elastic potential energy in its springy legs and then converts this potential energy in to kinetic energy at touchdown, when it “kicks off” a wall. This paper describes the ParkourBot's mechanical design, modeling, and open-loop climbing experiments. The mechanical design makes use of the BowLeg, previously used for hopping on a flat ground. We introduce two models of the BowLeg ParkourBot: one is based on a nonzero stance duration using the spring-loaded inverted pendulum model, and the other is a simplified model (the simplest parkour model, or SPM) obtained as the leg stiffness approaches infinity and the stance time approaches zero. The SPM approximation provides the advantage of closed-form calculations. Finally, predictions of the models are validated by experiments in open-loop climbing in a reduced-gravity planar environment provided by an air table.

This paper presents feedback stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We show that it is possible to stabilize the object at the upright position, while the hand or object rotates to a specific orientation or spins at a constant velocity. We use full-state feedback linearization to derive control laws. We present simulation as well as experimental results demonstrating the controllers.

This paper presents a hybrid mechanical model for the Gibbot, a robot that dynamically locomotes along a vertical wall in a manner analogous to gibbons swinging between branches in the forest canopy. We focus on one particular gait, continuous-contact brachiation, which always has one handhold in contact with the wall. We use zero-cost, unstable solutions corresponding to horizontal brachiation, originally found by Gomes and Ruina, as templates to generate open-loop stable gaits in arbitrary directions. The first case considered is passive brachiation down a shallow slope, roughly corresponding to upside-down locomotion of the well-studied compass-gait biped. We then consider underactuated brachiation with a constant forcing term at the elbow to produce open-loop stable descending and ascending gaits.

This paper presents stabilization control of a rolling manipulation system called the disk-on-disk. The system consists of two disks in which the upper disk (object) is free to roll on the lower disk (hand) under the influence of gravity. The goal is to stabilize the object at the unstable upright position directly above the hand. We use backstepping to derive a control law yielding global asymptotic stability. We present simulation as well as experimental results demonstrating the controller.

We present a method for controlling a neuroprosthesis for a paralyzed human arm using functional electrical stimulation (FES). The subject has surgically implanted electrodes for stimulating muscles in her shoulder and arm. Using input/output data, a model is identified that describes the mapping from muscle stimulations to the endpoint force measured at the subject's hand. To compute the muscle stimulations given a target endpoint force the model is inverted. Because the system is redundant, we compute the inverse by minimizing muscle activations and use this inverse for feedforward control. This is the first published demonstration with a human subject with a high spinal cord injury of an FES controller that treats the arm with shoulder and elbow as a multiple-input multiple-output system and can achieve arbitrary goals.

This paper explores the role of anisotropic friction properties in vibratory parts manipulation. We show that direction-dependent surface friction properties can be used in conjunction with a vibrating plate to help design friction-induced velocity fields on the surface of the plate. Theoretical, simulation, and experimental results are presented quantifying the anisotropic friction effects of textured surfaces such as micromachined silicon and fabrics.

The ParkourBot is an efficient and dynamic climbing robot. The robot comprises two springy legs connected to a body. Leg angle and spring tension are independently controlled. The robot climbs between two parallel walls by leaping from one wall to the other. During flight, the robot stores elastic energy in its springy legs and automatically releases the energy to "kick off" the wall during touch down. This paper elaborates on the mechanical design of the ParkourBot. We use a simple SLIP model to simulate the ParkourBot motion and stability. Finally, we detail experimental results, from open-loop climbing motions to closed-loop stabilization of climbing height in a planar, reduced gravity environment.

Hybrid dynamical systems with impacts typically have controls that can influence the time of the impact as well as the result of the impact. The leg angle of a hopping robot is an example of an impact control because it can influence when the impact occurs and the direction of the impulse. This paper provides a method for computing an explicit expression for the first derivative of a cost function encoding a desired trajectory. The first derivative can be used with standard optimization algorithms to find the optimal impact controls for motion planning of hybrid dynamical systems with impacts. The resulting derivation is implemented for a simplified model of a dynamic climbing robot.

A position-dependent asymptotic velocity field describes the motion of point parts sliding with friction on the surface of a rigid oscillating plate. These fields can be used to perform manipulation tasks such as sensorless positioning of one or several parts simultaneously. This paper examines the set of fields F generated by periodic plate motions M that combine a single in-plane component and a single out-of-plane component that have square wave accelerations with 50% duty cycles, identical periods, and an arbitrary phase between them. By deconstructing the full map Π : M → F into three simpler maps, we expose the structure of F and its relationship to M. To illustrate, we focus on particular plate motions in M that generate fields well approximated by polynomial functions of position with degree n ≤ 2. Numerical simulations suggest that fields generated from plate motions with more than a single inplane and a single out-of-plane component (all with the same period and square wave accelerations) are well approximated by linear combinations of fields in F.

We show that the frictional forces arising from simultaneous small amplitude periodic translation and rotation of a rigid plate cause parts on the plate to converge to or diverge from a line coinciding with the rotation axis. The relative phase between the translation and rotation determines whether the parts are attracted to or repelled from the rotation axis. Assuming that both the translational and rotational accelerations of the plate are ldquobang-bangrdquo and have identical frequencies, we derive the resultant velocity fields for point parts on the plate. For many choices of phase the speed of the part is approximately proportional to its distance from the rotation axis. The strength of the velocity field can be controlled by modulating the amplitude of the translational acceleration, or modulating the relative phase between the translational and rotational acceleration profiles. We also determine the phases that maximize part speed towards and away from the rotation axis. These optimal phases not only maximize part speed but also generate velocity fields that are nearly independent of the coefficient of friction.

We describe a vibratory part transport mechanism that utilizes both static and dynamic friction to linearly transport parts in a horizontal direction. We derive a horizontal driving profile for the feeder surface that maximizes the steady-state velocity of parts on the surface subject to acceleration limits on the surface. Experiments verify the predicted transport behavior. We then derive the optimal feeding motion for a surface that can move in both the horizontal and vertical directions.

Cooperating mobile sensors can be used to model environmental functions such as the temperature or salinity of a region of ocean. In this paper, we adopt an optimal filtering approach to fusing local sensor data into a global model of the environment. Our approach is based on the use of proportional-integral (PI) average consensus estimators, whereby information from each mobile sensor diffuses through the communication network. As a result, this approach is scalable and fully decentralized, and allows changing network topologies and anonymous agents to be added and subtracted at any time. We also derive control laws for mobile sensors to move to maximize their sensory information relative to current uncertainties in the model. The approach is demonstrated by simulations including modeling ocean temperature.

We explore the capabilities of a robot designed to locate objects underwater through active movement of an electric field emitter and sensor apparatus. The robot is inspired by the biological phenomenon of active electrolocation, a sensing strategy found in two groups of freshwater fishes known to emit weak electric fields for target localization and communication. We characterize the performance of the robot using several types of automatic electrolocation controllers, objects, and water conditions. We demonstrate successful electrolocation both in the conditions in which it is naturally observed, in low conductivity water, as well as in conditions in which it is not observed, in water of ocean salinity. The belief of the position of the target is maintained via a particle filter and refined with each measurement

By vibrating a rigid plate with up to six degrees of freedom, we can create a large family of programmable frictional force fields acting on parts resting on the plate. These fields can be used for sensorless part orientation, uncertainty-reducing transport, and simultaneous manipulation of multiple parts. The principle is demonstrated by a plate rotating about an axis below the plate. Simple oscillatory rotation produces a squeeze field that attracts and aligns parts along a center line. This behavior is confirmed in experiment. Motivated by this experimental confirmation, we use a simulation to find plate motions that yield a number of other useful primitive force fields. By sequencing these force fields, we can create any force field that is a convex combination of the primitives.

We consider the problem of multiple mobile sensor agents tracking the position of one or more moving targets. In our formulation, each agent maintains a target estimate, and each agent moves so as to maximize the expected information from its sensor, relative to the current uncertainty in the estimate. The novelty of our approach is that each agent need only communicate with one-hop neighbors in a communication network, resulting in a fully distributed and scalable algorithm, yet the performance of the system approximates that of a centralized optimal solution to the same problem. We provide two fully distributed algorithms based on one-time measurements and a Kalman filter approach, and we validate the algorithms with simulations.

In the Cobotic Hand Controller, we have introduced an admittance display that can render very high impedances (up to its own structural stiffness). This is due to its use of infinitely variable transmissions. While admittance displays typically excel at rendering high impedances, the incorporation of infinitely variable transmissions in the Cobotic Hand Controller allows the stable display of a wide dynamic range, including low impedances. The existence of a display that excels at rendering high-impedance constraints, but has high-fidelity control of low impedances tangent to those constraints, has led us to describe an admittance control architecture not often examined in the haptics community. In this paper, we develop a comprehensive approach that enables rendering of rigid motion constraints while simultaneously preserving the physical integrity of the intended inertial dynamics tangent to those constraints. This is in contrast to conventional impedance-control algorithms that focus primarily on rendering reaction forces along contact normals with constraints. We present this algorithm here, which is general to all admittance displays, and report on its implementation with the Cobotic Hand Controller. We offer examples of rigid bodies and linkages subject to holonomic and/or nonholonomic constraints

This paper studies the effect of communication link weighting schemes and long-range connections in speeding convergence to consensus on the average of the inputs to agents in a sensor network. Linear programming and LMI solutions are provided for the problem of centralized optimization of communication weights considering the possibility of intermittent bounded communication delays. Heuristic weighting schemes that can be implemented in a distributed fashion are also studied. Consensus convergence time may also be reduced by introducing long-range interactions, creating a "small world" network

This paper investigates motion planning for underactuated systems with impacts, as in legged robots. Some such systems admit decoupling vector fields between impacts, and the system can be thought of as a kinematic system as it moves along the integral curves of these decoupling vector fields. This reduces motion planning to choosing a sequence of decoupling vector fields and impact transition times between these vector fields. Each transition must satisfy the condition that the image of the pre-impact state (through the impact mapping) leads to a post-impact state aligned with the new decoupling vector field. We derive this condition, extending previous work where transitions were only allowed at zero velocity. Our approach combines the benefits of computationally efficient kinematic planning with potentially faster execution times due to the fact that the system does not have to be slowed to zero velocity at the switches. Switches are restricted to a lower-dimensional configuration surface, however. We have applied this approach to motion planning for a planar two-link robot which locomotes by using a single revolute actuator at the joint between the links and by alternately clamping one of two possible pivot points to the ground

This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible): any force necessary to preserve the assembly can be generated by the pushing contacts; (I = impossible): pushing forces cannot preserve the assembly; and (U = undecided): pushing forces may or may not be able to preserve the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the part-part and part-pusher contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given

This paper presents a method to determine whether an assembly of planar parts will stay assembled as it is pushed over a support surface. For a given pushing motion, an assembly is classified into one of three categories: (P = possible) any force necessary to assure stability of the assembly can be generated by the pushing contacts; (I = impossible) stability of the assembly is impossible; and (U = undecided) pushing forces may or may not be able to stabilize the assembly. This classification is made based on the solution of linear constraint satisfaction problems. If the pushing contacts are frictionless, motions labeled P are guaranteed to preserve the assembly. The results are based on bounds on the possible support friction acting on individual parts in the face of indeterminacy in the distribution of support forces. Experimental results supporting the analysis are given.

In this paper we are concerned with allowing the operator of a haptic display to interact with virtual systems having significant inertial dynamics and realistic constraints. We review the mathematical structure arising from the kinetic energy metric, required to create a virtual dynamics simulation consisting of rigid-body dynamics along with holonomic and/or nonholonomic motion constraints. We develop an admittance controller composed of feedforward and feedback terms, while preserving the integrity of the intended virtual dynamics simulation. This controller is implemented on the Cobotic Hand Controller, an admittance-type haptic display, and two examples are discussed.

Throwing and catching parts, similar to vibratory agitation, promises to be a powerful manipulation technique, but is analytically complicated by equations of motion involving friction and impacts. However, one can show that some simple part manipulators exhibit limit set behavior, where the parts enter a set that is invariant under the mapping that corresponds to the throwing action. We show that by analyzing limit sets directly we can design parts and their environment so that part feeding or assembling naturally emerges from the dynamics. We include experiments validating both these approaches and a discussion of future work.

We study the problem of generating motion plans for kinematically controllable underactuated systems in environments cluttered with obstacles. We develop a computationally efficient motion planning algorithm that finds fast trajectories by exploiting closed-form inverse kinematics of the robot. The completeness property of the motion planning algorithm can be proven using appropriate metrics defined in the configuration space of the kinematically controllable systems. The snakeboard is used as an example of a kinematically controllable underactuated system to test the motion planning algorithm, and motion plans have been implemented on an experimental snakeboard.

This study investigates natural single-arm interaction with kinematic constraints. Smooth, frictionless, kinematic constraints reduce the degrees-of-freedom of motion at the hand, but add force freedoms. These force freedoms allow the hand to push and pull against the constraints with no effect on the task. Understanding how subjects take advantage of kinematic constraints will be useful in designing constraint surfaces for assisted manipulation. This paper reports the results of an experiment studying how subjects make use of the presence of a kinematic constraint in a static planar single-arm task. Subjects are asked to hold a handle that is free to slide on a linear rail, and to apply a force tangent to the rail to resist a pulling force. Thus the goal of the task is to hold the handle stationary. Subjects are also free to apply any force normal to the rail, as these forces have no effect on the task. This freedom does not exist without a kinematic constraint. We find that subjects make use of the force freedom by applying significant forces against the constraint in a consistent and constraint-configuration-dependent fashion. We show that the constraint forces can be predicted by a convex, scale-invariant objective function on the hand force space. The level curves of this objective function can be found directly from the experimental data without any biomechanical modeling.

We have been exploring the use of passive robotic mechanisms for the display of virtual surfaces. Cobots are one way of producing virtual surfaces using a passive mechanism. Unlike powered robots, the nonlinear dynamics of the passive mechanism (e.g., an arm) can be felt by the user as a spatially varying apparent inertia. This effect occurs in many passive designs, including but not limited to cobots. We explain the variable apparent inertia as the projection of the spatially-varying inertia matrix onto the direction of motion, and discuss several ways to control the apparent inertia. We explore apparent inertia in detail for the unicycle two link arm, a cobot we have developed for experiments in single-arm motor control studies and rehabilitation. Special paths ("iso-mass contours") are found for this mechanism along which the apparent inertia is constant.

This work presents a method to determine stable pushing motions for a planar stack of polygonal parts. The approach consists of solving a series of subproblems where each part in the stack is pushing the parts ahead of it. The solutions to these subproblem an sets of stable motions, and their intersection is the set of stable motions for the entire stack. The motion of multiple parts depends on the exact locations of the centers of mass and the relative masses of the parts. If either or both of these is unknown, it is still possible to calculate a conservative set of motions guaranteed to be stable by using a center of mass uncertainty region. Local-local controllability is also analyzed for single parts and stocks of parts with uncertain centers of mass. Once parts have been brought together in an automated assembly sequence, they typically must be repositioned to complete fastening or welding operations. This can be done with powerful robots capable of grasping and carrying the assembly and may involve a unique fixture to maintain the assembly during transport. A cheaper and more flexible alternative is to use a less powerful robot that can push the assembly along a horizontal surface without the aid of fixtures. This work presents a graphical method that produces conservative bounds on the pushing motions that guarantee the stability of a linear assembly (i.e., a stock of parts) during the push. The main application is in motion planning for assembly sequencing but the results could also he useful, for example, for mobile robots pushing multiple boxes in a warehouse. The method can be made robust to uncertainty in The mass properties of the parts, such as boxes with unknown contents. It is limited to linear stacks of parts where each part pushes no more than one other part In future work, we plan to devise a method to compute stable pushing motions for arbitrary assemblies of parts.

We study the problem of computing an exact motion plan for the snakeboard, an underactuated system subject to nonholonomic constraints, by exploiting its kinematic controllability properties and its decoupling vector fields. Decoupling vector fields allow us to plan motions for the underactuated dynamic system as if it were kinematic, and rest-to-rest paths are the concatenation of integral curves of the decoupling vector fields. These paths can then be time-scaled according to actuator limits to yield fast trajectories. Switches between decoupling vector fields must occur at zero velocity, so, to find fast trajectories, we wish to find paths minimizing the number of switches. In this paper, we solve the minimum-switch path-planning problem for the snakeboard. We consider two problems: 1) finding motion plans achieving a desired position and orientation of the body of the snakeboard and 2) the full problem of motion planning for all five configuration variables of the snakeboard. The first problem is solvable in closed form by geometric considerations, while the second problem is solved by a numerical approach with guaranteed convergence. We present a complete characterization of the snakeboard's minimum-switch paths.

This paper presents a method to determine stable pushing motions for a planar stack of polygonal parts. The approach consists of solving a series of subproblems where each part in the stack is pushing the parts ahead of it. The solutions to these subproblems are sets of stable motions, and their intersection is the set of stable motions for the entire stack. The motion of multiple parts depends on the exact locations of the centers of mass and the relative masses of the parts. If either or both of these is unknown, it is still possible to calculate a conservative set of motions guaranteed to be stable by using a center of mass uncertainty region.

We study the problem of computing an exact motion plan for the snakeboard by exploiting its kinematic controllability properties and its decoupling vector fields. Decoupling vector fields allow us to treat the underactuated dynamic system as a kinematic one, and rest-to-rest paths are the concatenation of integral curves of the decoupling vector fields. These paths can then be time-scaled according to actuator limits to yield fast trajectories. Switches between decoupling vector fields must occur at zero velocity, so to find fast trajectories, we wish to find paths minimizing the number of switches. In this paper we solve the minimum switch path planning problem for the snakeboard. We consider two problems: (1) finding motion plans achieving a desired position and orientation of the body of the snakeboard, and (2) the full problem of motion planning for all five configuration variables of the snakeboard. The first problem is solved in closed form by geometric considerations, while the second problem is solved by a numerical approach with guaranteed convergence. We present a complete characterization of the snakeboard's optimal paths in terms of the number of switches.

Of several possible forms of human-robot collaborative manipulation, we focus on the case where the human and the robot jointly manipulate a common load. In our formulation, the robot's role is to provide a constraint surface to guide the motion of the load. The value of this form of interaction, in terms of ergonomics, accuracy, or speed, depends on how humans make use of such constraints. We are studying natural single-arm manipulation of a load constrained to move along a guide rail. In this paper we present results of experiments showing that subjects apply significant forces against the rail, depending on the configuration of the arm and the orientation of the rail. These forces are unnecessary for the manipulation task, and we hypothesize that humans apply forces against the constraint to simplify the manipulation task.

We describe a one-joint planar arm which repeatedly throws and catches parts on its surface, and we demonstrate that proper choice of the throw velocity and arm geometry guarantees that the part will enter a unique recurrent motion pattern from a large set of initial configurations. The resulting system resembles an open-loop stable juggler of polygonal parts. Combined with a simple 1-bit sensor, the system can be used as a parts feeder.

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collision-free trajectory planning for a broad class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.

We describe a one-joint planar arm which repeatedly throws and catches parts on its surface, and we demonstrate that proper choice of the throw velocity and arm geometry guarantees that the part will enter a unique recurrent motion pattern from a large set of initial configurations. The resulting system resembles an open-loop stable juggler of polygonal parts.

We introduce the notion of kinematic controllability for second-order underactuated mechanical systems. For systems satisfying this property, the problem of planning fast collision-free trajectories between zero velocity states can be decoupled into the computationally simpler problems of path planning for a kinematic system followed by time-optimal time scaling. While this approach is well known for fully actuated systems, until now there has been no way to apply it to underactuated dynamic systems. The results in this paper form the basis for efficient collision-free trajectory planning for a class of underactuated mechanical systems including manipulators and vehicles in space and underwater environments.

This paper applies the idea of forced recurrence to demonstrate controllability and stabilizability of a single-input juggling system. Nonlinear optimization is used to find controls in a neighborhood of the recurrent controls that drive the system toward the goal trajectory. The approach is demonstrated on an experimental juggling system.

This paper investigates the controllability of underactuated rolling systems consisting of a smooth object rolling on a moving smooth surface. Our system consists of a spherical ball which rolls on the inside of an ellipsoidal bowl. The bowl has a single translational degree of freedom not aligned with any of its principal axes. The single control input is the bowl's acceleration in this direction. The object and contact motions are governed by a nonlinear system of equations derived from the kinematics and dynamics of rolling. Using existing results on small time local accessibility and weakly positive Poisson stable vector fields, and assuming that the ball stays in the bowl, we show that the ball is globally controllable on its five-dimensional space of configurations relative to the bowl. Our next step is on motion planning algorithms with our experimental setup to control the equilibrium configuration of the ball.

Manual materials handling of heavy loads is a common cause of low back disorders. The manual manipulation of a heavy load may be made more comfortable by constraining the load to move along a guide. If the load is constrained the human operator can provide forces in directions that are comfortable while the frictionless guide directs the motion of the load to the goal configuration. We study the design of such motion guides for ergonomic materials handling. We formulate the problem and provide some example guides for planar manipulation. The motion guides may be implemented by fixed rail systems or by programmable constraint machines (cobots).

Repetitive manual materials handling of heavy loads is common in assembly and is a common cause of low back disorders. The manual manipulation of a heavy load may be made more comfortable by constraining the load to move along a guide. The frictionless guide directs the motion of the load to the goal configuration as the human operator provides forces in directions that are comfortable. We present our first experimental results in guided manipulation with the purpose of understanding motions and forces that are comfortable for human operators.

This paper describes a robotic manipulation primitive called toppling, i.e. knocking a part over. We derive the mechanical conditions for toppling, express these as constraints on robot contact locations and motions, and describe an application of toppling to minimalist parts feeding of 3D objects on a conveyor with a 2 joint robot.

When a polygonal object is pushed with line contact along an edge, the push is called stable if the object remains fixed to the pusher. The object is small-time locally controllable by stable pushing if, by switching among pushing edges, it can be pushed to follow any path arbitrarily closely. Since the pushes are stable by the frictional mechanics, pushing plans can be executed without position feedback of the object. We derive a necessary and sufficient condition for a polygon to be small-time locally controllable by stable pushing: the pushing friction coefficient must be nonzero and the set of feasible pure forces (forces applied through a polygon edge and passing through the center of friction) must positively span the plane. We interpret this condition in terms of the polygon shape, the location of the center of friction, and the pushing friction coefficient, allowing us to characterize classes of polygons with this fundamental "manoeuvrability" property.

Studies motion planning from one zero velocity state to another for a three-joint robot in a horizontal plane with a passive revolute third joint. Such a robot is small-time locally controllable on an open subset of its zero velocity section, allowing it to follow any path in this subset arbitrarily closely. However some paths are "preferred" by the dynamics of the manipulator in that they can be followed at higher speeds. We describe an algorithm that plans collision-free paths in the robot's configuration space, where the motions correspond to dynamically preferred robot motions. Thus the problem of planning fast trajectories in the robot's six-dimensional state space is reduced to the computationally simpler problems of planning paths in the three-dimensional configuration space and time-scaling the paths according to the manipulator dynamics. Implementation on an underactuated manipulator is described.

We study the juggler skill called the "butterfly". Starting with a ball resting on the palm of his/her open hand, a skilled juggler can accelerate and shape his/her hand so that the ball rolls up the fingers, over the top, and back down to the back of the hand. This paper describes a robotic implementation of the butterfly. The combined hand shape and motion set the rolling motion of the ball, and we find that the shape and motion parameters enter the dynamic equations in a similar way. We define parametrized spaces of hand shape and motion, and using a simulation based on the rolling equations, we identify shape and motion solutions that roll the ball from one side of the hand to the other. We describe an implementation of the butterfly on our planar dynamic manipulation testbed FLATLAND. This example is our first step toward exploring the roles of shape and motion in dynamic manipulation.

This paper explores a sensorless technique for orienting planar parts. We follow an approach described in the ours earlier papers (1995), called one joint over conveyor (1JOC), which can perform planar manipulation using a single controlled joint in combination with a constant-velocity conveyor. Our previous work demonstrated that the IJOC approach can orient and feed planar polygonal parts, given a singulated part in a known initial location. This paper shows that a variation called the sensorless IJOC can orient and feed polygonal parts up to symmetries in the underlying mechanics, without knowing the initial location and without sensors.

This paper characterizes polygons that are small-time locally controllable by stable pushing as a function of the polygon shape, the location of the center of friction, and the friction coefficient at the pushing contact. Such polygons can be pushed to follow any path arbitrarily and closely, a useful property for planar manipulation. Because the pushes are stable, pushing plans can be executed without feedback.

We are interested in using low degree-of-freedom robots to perform complex manipulation task without grasping. The robot can use rolling, slipping, and free flight to control more degrees-of-freedom of the part. To demonstrate this we study the controllability properties of planar dynamic nonprehensile manipulation. We show that almost any planar object is small-time locally controllable by point contact, and the controlling robot requires only two degrees-of-freedom (a point translating in the plane). We then focus on a one joint manipulator (with a two-dimensional state space) and show that even this simplest of robots, by using slipping and rolling, can control an object to a full-dimensional subset of its six-dimensional state space. We have developed a one joint robot to perform a variety of dynamic tasks, including snatching an object from a table, rolling an object on the surface of the arm, and throwing and catching.

By exploiting centrifugal and Coriolis forces, simple, low-degree-of-freedom robots can control objects with more degrees-of-freedom. For example, by allowing the object to roll and slip, a one-degree-of-freedom revolute robot can take a planar object to a full-dimensional subset of its state space. We present a dynamic manipulation planner that finds manipulator trajectories to move an object from one state to another without grasping it. The trajectories have been successfully implemented on a one-degree-of-freedom direct drive arm to perform dynamic tasks such as snatching an object from a table, rolling an object on the surface of the arm, and throwing and catching.

This paper addresses the question "Can the object be pushed from here to there?" The authors characterize the set of objects that are controllable (can be positioned arbitrarily), with and without obstacles, for the cases of point and line pushing contact. For the case of line contact, the authors find a set of pushing directions that keep the object fixed to the pusher and they use these pushing directions to find sensorless plans to reposition the object among obstacles.

In order to plan manipulation of an object by pushing, a robot must have a model of the geometry and the friction properties of the object. This paper presents an approach to estimating the relevant friction parameters by performing experimental pushes and observing the resultant motion. Recognition of objects based on their friction parameters is also explored.

Dynamic manipulation is defined, and a brief survey of dynamic operations is given. The design, control, and planning of dynamic manipulation is addressed. An example of dynamic manipulation, club-throwing using dynamic closure, is described.

The author presents a method for determining the possible instantaneous motions of a sliding object during multiple contact pushing. The approach consists of two components: a kinematic analysis considering kinematic motion constraints, and a force analysis considering force constraints on the motion. A representation of the support friction of a sliding object is presented, and the results of the force analysis are independent of the exact support distribution of the object. The analysis results in a manipulation primitive: stable rotational pushing. This primitive may be used for precise placement operations by pushing.>

Abstract — We investigate manipulation and active sensing by a pushing control system using only tactile feedback. The equations of motion of a pushed object are derived using a model of the object’s limit surface, and we design a control system to translate and orient objects. The effectiveness of the proposed controller is confirmed through simulation and experiments. Active sensing of the object’s center of mass is described. I.