Modern legged robot morphologies assign most of their actuated degrees of freedom (DoF's) to the limbs and designs continue to converge to twelve DoF quadrupeds with three actuators per leg and a rigid torso often modeled as a Single Rigid Body (SRB). This is in contrast to the animal kingdom, which provides tantalizing hints that core actuation of a jointed torso confers substantial benefit for efficient agility. Unfortunately, the limited specific power of available actuators continues to hamper roboticists' efforts to capitalize on this bio-inspiration. This paper presents the initial steps in a comparative study of the costs and benefits associated with a traditionally neglected torso degree of freedom: a twisting spine. We use trajectory optimization to explore how a one-DoF, axially twisting spine might help or hinder a set of axially-active (twisting) behaviors: trots, sudden turns while bounding, and parkour-style wall jumps. By optimizing for minimum electrical energy or average power, intuitive cost functions for robots, we avoid hand-tuning the behaviors and explore the activation of the spine. Initial evidence suggests that for lower energy behaviors the spine increases the electrical energy required when compared to the rigid torso, but for higher energy runs the spine trends toward having no effect or reducing the electrical work. These results support future, more bio-inspired versions of the spine with inherent stiffness or dampening built into their mechanical design.

This paper introduces a new controller that stabilizes the motion of a spatial quadruped around sagittal-plane templates. It enables highly dynamic gaits and transitional maneuvers formed from parallel and sequential compositions of such planar templates in settings that require significant out-of-plane reactivity. The controller admits formal guarantees of stability with some modest assumptions. Experimental results validate the reliable execution of those planar template-based maneuvers, even in the face of large lateral, yaw, and roll incurring disturbances. This spatial anchor, fixed in parallel composition with a variety of different parallel and sequential compositions of sagittal plane templates, illustrates the robust portability of provably interoperable modular control components across a variety of hardware platforms and behaviors.

Origami processes can generate both rigid and compliant structures from the same homogeneous sheet material. In this article, we advance the origami robotics literature by showing that it is possible to construct an arbitrary rigid kinematic chain with prescribed joint compliance from a single tubular sheet. Our “Kinegami” algorithm converts a Denavit–Hartenberg specification into a single-sheet crease pattern for an equivalent serial robot mechanism by composing origami modules from a catalogue. The algorithm arises from the key observation that tubular origami linkage design reduces to a Dubins path planning problem. The automatically generated structural connections and movable joints that realize the specified design can also be endowed with independent user-specified compliance. We apply the Kinegami algorithm to a number of common robot mechanisms and hand-fold their algorithmically generated single-sheet crease patterns into functioning kinematic chains. We believe this is the first completely automated end-to-end system for converting an abstract manipulator specification into a physically realizable origami design that requires no additional human input.

We describe a task and motion planning architecture for highly dynamic systems that combines a domain-independent sampling-based deliberative planning algorithm with a global reactive planner. We leverage the recent development of a reactive, vector field planner that provides guarantees of reachability to large regions of the environment even in the face of unknown or unforeseen obstacles. The reachability guarantees can be formalized using contracts that allow a deliberative planner to reason purely in terms of those contracts and synthesize a plan by choosing a sequence of reactive behaviors and their target configurations, without evaluating specific motion plans between targets. This reduces both the search depth at which plans will be found, and the number of samples required to ensure a plan exists, while crucially preserving correctness guarantees. The result is reduced computational cost of synthesizing plans, and increased robustness of generated plans to actuator noise, model misspecification, or unknown obstacles. Simulation studies show that our hierarchical planning and execution architecture can solve complex navigation and rearrangement tasks, even when faced with narrow passageways or incomplete world information.

Complex manipulation tasks, such as rearrangement planning of numerous objects, are combinatorially hard problems. Existing algorithms either do not scale well or assume a great deal of prior knowledge about the environment, and few offer any rigorous guarantees. In this paper, we propose a novel hybrid control architecture for achieving such tasks with mobile manipulators. On the discrete side, we enrich a temporal logic specification with mobile manipulation primitives such as moving to a point, and grasping or moving an object. Such specifications are translated to an automaton representation, which orchestrates the physical grounding of the task to mobility or manipulation controllers. The grounding from the discrete to the continuous reactive controller is online and can respond to the discovery of unknown obstacles or decide to push out of the way movable objects that prohibit task accomplishment. Despite the problem complexity, we prove that, under specific conditions, our architecture enjoys provable completeness on the discrete side, provable termination on the continuous side, and avoids all obstacles in the environment. Simulations illustrate the efficiency of our architecture that can handle tasks of increased complexity while also responding to unknown obstacles or unanticipated adverse configurations.

In this article, we physically demonstrate a reactive sensorimotor architecture for mobile robots whose behaviors are generated by motivation dynamics. Motivation dynamics uses a continuous dynamical system to reactively compose low-level control vector fields using valuation functions that capture the potentially competing influences of external stimuli relative to the system's own internal state. We show that motivation dynamics naturally accommodates external stimuli through standard signal processing tools, and can effectively encode a repetitive higher level task by composing several low-level controllers to achieve a limit cycle in which the robot repeatedly navigates toward two alternatively valuable goal locations in a commensurately alternating order. We show that these behaviors are robust to perturbations, including imperfect models of robot kinematics, sensor noise, and disturbances, resulting from the need to traverse difficult terrain. We argue that motivation dynamics can provide a useful alternative to controllers based on hybrid automata in situations where the control operates at a low level close to the physical hardware.

Despite substantial evidence for the crucial role played by an active backbone or spine in animal locomotion, its adoption in legged robots remains limited because the added mechanical complexity and resulting dynamical challenges pose daunting obstacles to characterizing even a partial range of potential performance benefits. This paper takes a next step toward such a characterization by exploring the quasistatic terrestrial self-righting mechanics of a model system with coronal plane spine twisting (CPST). Reduction from a full 3D kinematic model of CPST to a two parameter, two degree of freedom coronal plane representation of body shape affordance predicts a substantial benefit to ground righting by lowering the barrier between stable potential energy basins. The reduced model predicts the most advantageous twist angle for several cross-sectional geometries, reducing the required righting torque by up to an order of magnitude depending on constituent shapes. Experiments with a three actuated degree of freedom physical mechanism corroborate the kinematic model predictions using two different quasistatic reorientation maneuvers for both elliptical and rectangular shaped bodies with a range of eccentricities or aspect ratios. More speculative experiments make intuitive use of the kinematic model in a highly dynamic maneuver to suggest still greater benefits of CPST achievable by coordinating kinetic as well as potential energy, for example as in a future multi-appendage system interacting with a contact-rich 3D environment.

We work with geoscientists studying erosion and desertification to improve the spatial and temporal resolution of their data collection over long transects in difficult realworld environments such as deserts [1]. The Minitaur [2] robot, which can run quickly over uneven terrain and use a single leg to measure relevant ground properties such as stiffness [3], is an attractive scout robot candidate for inclusion in a heterogeneous team in collaboration with a heavily geared, sensor-laden RHex [4]. However, Minitaur is challenged by long-distance locomotion on sand dunes. Previous simulation results [5] suggested that the energetic cost of transport can be mitigated by programming a virtual damping force to slow the intrusion of a Minitaur foot into simulated granular media following a bulk-behavior force law [6]. In this paper, we present a ground emulator that can be used to test such locomotion hypotheses with a physical single-legged hopper jumping on emulated ground programmed to exhibit any compliance and damping characteristics of interest. The new emulator allows us to corroborate the conclusions of our previous simulation with physical hopping experiments. Programming the substrate emulator to exhibit the mechanics of a simplified bulk-behavior model of granular media characterized by linear stiffness and quadratic damping, we achieve a consistent energy savings of 20% in comparison with a nominal controller, with savings of up to 50% under specific conditions.

A challenge of pan/tilt/zoom (PTZ) camera networks for efficient and flexible visual monitoring is automated active network reconfiguration in response to environmental stimuli. In this paper, given an event/activity distribution over a convex environment, we propose a new provably correct reactive coverage control algorithm for PTZ camera networks that continuously (re) configures camera orientations and zoom levels (i.e., angles of view) in order to locally maximize their total coverage quality. Our construction is based on careful modeling of visual sensing quality that is consistent with the physical nature of cameras, and we introduce a new notion of conic Voronoi diagrams, based on our sensing quality measures, to solve the camera network allocation problem: that is, to determine where each camera should focus in its field of view given all the other cameras' configurations. Accordingly, we design simple greedy gradient algorithms for both continuous-and discrete-time first-order PTZ camera dynamics that asymptotically converge a locally optimal coverage configuration. Finally, we provide numerical and experimental evidence demonstrating the effectiveness of the proposed coverage algorithms.

The efficiency of sampling-based motion planning algorithms is dependent on how well a steering procedure is capable of capturing both system dynamics and configuration space geometry to connect sample configurations. This paper considers how metrics describing local system dynamics may be combined with convex subsets of the free space to describe the local behavior of a steering function for sampling-based planners. Subsequently, a framework for using these subsets to extend the steering procedure to incorporate this information is introduced. To demonstrate our framework, three specific metrics are considered: the LQR cost-to-go function, a Gram matrix derived from system linearization, and the Mahalanobis distance of a linear-Gaussian system. Finally, numerical tests are conducted for a second-order linear system, a kinematic unicycle, and a linear-Gaussian system to demonstrate that our framework increases the connectivity of sampling-based planners and allows them to better explore the free space.

This paper considers the problem of completing assemblies of passive objects in nonconvex environments, cluttered with convex obstacles of unknown position, shape and size that satisfy a specific separation assumption. A differential drive robot equipped with a gripper and a LIDAR sensor, capable of perceiving its environment only locally, is used to position the passive objects in a desired configuration. The method combines the virtues of a deliberative planner generating high-level, symbolic commands, with the formal guarantees of convergence and obstacle avoidance of a reactive planner that requires little onboard computation and is used online. The validity of the proposed method is verified both with formal proofs and numerical simulations.

We present the first fully spatial hopping gait of a 12 DoF tailed biped driven by only 4 actuators. The control of this physical machine is built up from parallel compositions of controllers for progressively higher DoF extensions of a simple 2 DoF, 1 actuator template. These template dynamics are still not themselves integrable, but a new hybrid averaging analysis yields a conjectured closed form representation of the approximate hopping limit cycle as a function of its physical and control parameters. The resulting insight into the role of the machines kinematic and dynamical design choices affords a redesign leading to the newly achieved behavior.

We demonstrate the physical rearrangement of wheeled stools in a moderately cluttered indoor environment by a quadrupedal robot that autonomously achieves a user's desired configuration. The robot's behaviors are planned and executed by a three layer hierarchical architecture consisting of: an offline symbolic task and motion planner; a reactive layer that tracks the reference output of the deliberative layer and avoids unanticipated obstacles sensed online; and a gait layer that realizes the abstract unicycle commands from the reactive module through appropriately coordinated joint level torque feedback loops. This work also extends prior formal results about the reactive layer to a broad class of nonconvex obstacles. Our design is verified both by formal proofs as well as empirical demonstration of various assembly tasks.

In robotics, it is often practically and theoretically convenient to design motion planners for approximate low-order (e.g., position-or velocity-controlled) robot models first, and then adapt such reference planners to more accurate high-order (e.g., force/torque-controlled) robot models. In this paper, we introduce a novel provably correct approach to extend the applicability of low-order feedback motion planners to high-order robot models, while retaining stability and collision avoidance properties, as well as enforcing additional constraints that are specific to the high-order models. Our smooth extension framework leverages the idea of reference governors to separate the issues of stability and constraint satisfaction, affording a bidirectionally coupled robot-governor system where the robot ensures stability with respect to the governor and the governor enforces state (e.g., collision avoidance) and control (e.g., actuator limits) constraints. We demonstrate example applications of our framework for augmenting path planners and vector field planners to the second-order robot dynamics.

We document empirically stable bounding using an actively powered spine on the Inu quadrupedal robot, and propose a reduced-order model to capture the dynamics associated with this additional, actuated spine degree of freedom. This model is sufficiently accurate as to roughly describe the robots mass center trajectory during a bounding limit cycle, thus making it a potential option for low dimensional representations of spine actuation in steady-state legged locomotion.

This paper contributes to quantifying the notion of robotic fitness by developing a set of necessary conditions that determine whether a small quadruped has the ability to open a class of doors or climb a class of stairs using only quasi-static maneuvers. After verifying that several such machines from the recent robotics literature are mismatched in this sense to the common human scale environment, we present empirical work-arounds for the Minitaur quadrupedal platform that enable it to leap up, force the door handle and push through the door, as well as bound up the stairs, thereby accomplishing through dynamical maneuvers otherwise (i.e., quasi-statically) unachievable tasks.

Sampling-based algorithms offer computationally efficient, practical solutions to the path finding problem in high-dimensional complex configuration spaces by approximately capturing the connectivity of the underlying space through a (dense) collection of sample configurations joined by simple local planners. In this paper, we address a long-standing bottleneck associated with the difficulty of finding paths through narrow passages. Whereas most prior work considers the narrow passage problem as a sampling issue (and the literature abounds with heuristic sampling strategies) very little attention has been paid to the design of new effective local planners. Here, we propose a novel sensory steering algorithm for sampling-based motion planning that can “feel” a configuration space locally and significantly improve the path planning performance near difficult regions such as narrow passages. We provide computational evidence for the effectiveness of the proposed local planner through a variety of simulations which suggest that our proposed sensory steering algorithm outperforms the standard straight-line planner by significantly increasing the connectivity of random motion planning graphs.

We reconsider the problem of reactive navigation in sphere worlds, i.e., the construction of a vector field over a compact, convex Euclidean subset punctured by Euclidean disks, whose flow brings a Euclidean disk robot from all but a zero measure set of initial conditions to a designated point destination, with the guarantee of no collisions along the way. We use power diagrams, generalized Voronoi diagrams with additive weights, to identify the robot's collision free convex neighborhood, and to generate the value of our proposed candidate solution vector field at any free configuration via evaluation of an associated convex optimization problem. We prove that this scheme generates a continuous flow with the specified properties. We also propose its practical extension to the nonholonomically constrained kinematics of the standard differential drive vehicle.

In distributed mobile sensing applications, networks of agents that are heterogeneous, respecting both actuation as well as body and sensory footprint, are often modelled by recourse to power diagrams - generalized Voronoi diagrams with additive weights. In this paper, we adapt the body power diagram to introduce its “free subdiagram,” generating a vector field planner that solves the combined sensory coverage and collision avoidance problem via continuous evaluation of an associated constrained optimization problem. We propose practical extensions (a heuristic congestion manager that speeds convergence and a lift of the point particle controller to the more practical differential drive kinematics) that maintain the convergence and collision guarantees.

Spatial point process models are a commonly-used statistical tool for studying the distribution of objects of interest in a domain. We study the problem of deploying mobile robots as remote sensors to estimate the parameters of such a model, in particular the intensity parameter λ which measures the mean density of points in a Poisson point process. This problem requires covering an appropriately large section of the domain while avoiding the objects, which we treat as obstacles. We develop a control law that covers an expanding section of the domain and an online criterion for determining when to stop sampling, i.e., when the covered area is large enough to achieve a desired level of estimation accuracy, and illustrate the resulting system with numerical simulations.

The Jerboa, a tailed bipedal robot with two hip-actuated, passive-compliant legs and a doubly actuated tail, has been shown both formally and empirically to exhibit a variety of stable hopping and running gaits in the sagittal plane. In this paper we take the first steps toward operating Jerboa as a fully spatial machine by addressing the predominant mode of destabilization away from the sagittal plane: body roll. We develop a provably stable controller for underactuated aerial stabilization of the coupled body roll and tail angles, that uses just the tail torques. We show that this controller is successful at reliably reorienting the Jerboa body in roughly 150 ms of freefall from a large set of initial conditions. This controller also enables (and appears intuitively to be crucial for) sustained empirically stable hopping in the frontal plane by virtue of its substantial robustness against destabilizing perturbations and calibration errors. The controller as well as the analysis methods developed here are applicable to any robotic platform with a similar doubly-actuated spherical tail joint.

We introduce the use of hierarchical clustering for relaxed deterministic coordination and control of multiple robots. Traditionally, an unsupervised learning method, hierarchical clustering offers a formalism for identifying and representing spatially cohesive and segregated robot groups at different resolutions by relating the continuous space of configurations to the combinatorial space of trees. We formalize and exploit this relation, developing computationally effective reactive algorithms for navigating through the combinatorial space in concert with geometric realizations for a particular choice of the hierarchical clustering method. These constructions yield computationally effective vector field planners for both hierarchically invariant as well as transitional navigation in the configuration space. We apply these methods to the centralized coordination and control of n perfectly sensed and actuated Euclidean spheres in a d-dimensional ambient space (for arbitrary n and d). Given a desired configuration supporting a desired hierarchy, we construct a hybrid controller that is quadratic in n and algebraic in d and prove that its execution brings all but a measure zero set of initial configurations to the desired goal, with the guarantee of no collisions along the way.

This paper develops a comparative framework for the design of actuated inertial appendages for planar aerial reorientation. We define the inertial reorientation template, the simplest model of this behavior, and leverage its linear dynamics to reveal the design constraints linking a task with the body designs capable of completing it. As practicable inertial appendage designs lead to morphology that is generally more complex, we advance a notion of “anchoring,” whereby a judicious choice of physical design in concert with an appropriate control policy yields a system whose closed-loop dynamics are sufficiently captured by the template to permit all further designs to take place in its far simpler parameter space. This approach is effective and accurate over the diverse design spaces afforded by existing platforms, enabling a performance comparison through the shared task space. We analyze examples from the literature and find advantages to each body type, but conclude that tails provide the highest potential performance for reasonable designs. Thus motivated, we build a physical example by retrofitting a tail to a RHex robot and present empirical evidence of its efficacy.

We have built a 4DOF tailed monoped that hops along a boom permitting free sagittal plane motion. This underactuated platform is powered by a hip motor that adjusts leg touchdown angle in flight and balance in stance, along with a tail motor that adjusts body shape in flight and drives energy into the passive leg shank spring during stance. The motor control signals arise from the application in parallel of four simple, completely decoupled 1DOF feedback laws that provably stabilize in isolation four corresponding 1DOF abstract reference plants. Each of these abstract 1DOF closed loop dynamics represents some simple but crucial specific component of the locomotion task at hand. We present a partial proof of correctness for this parallel composition of “template” reference systems along with data from the physical platform suggesting these templates are “anchored” as evidenced by the correspondence of their characteristic motions with a suitably transformed image of traces from the physical platform.

This paper explores the design space of simple legged robots capable of leaping culminating in new behaviors for the Penn Jerboa, an underactuated, dynamically dexterous robot. Using a combination of formal reasoning and physical intuition, we analyze and test successively more capable leaping behaviors through successively more complicated body mechanics. The final version of this machine studied here bounds up a ledge 1.5 times its hip height and crosses a gap 2 times its body length, exceeding in this last regard the mark set by the far more mature RHex hexapod. Theoretical contributions include a non-existence proof of a useful class of leaps for a stripped-down initial version of the new machine, setting in motion the sequence of improvements leading to the final resulting performance. Conceptual contributions include a growing understanding of the Ground Reaction Complex as an effective abstraction for classifying and generating transitional contact behaviors in robotics.

This paper examines the design of a parallel spring-loaded actuated linkage intended for dynamically dexterous legged robotics applications. Targeted at toe placement in the sagittal plane, the mechanism applies two direct-drive brushless dc motors to a symmetric five bar linkage arranged to power free tangential motion and compliant radial motion associated with running, leaping, and related agile locomotion behaviors. Whereas traditional leg design typically decouples the consideration of motor sizing, kinematics and compliance, we examine their conjoined influence on three key characteristics of the legged locomotion cycle: transducing battery energy to body energy during stance; mitigating collision losses upon toe touchdown; and storing and harvesting prior body energy in the spring during stance. This analysis leads to an unconventional design whose “knee” joint rides above the “hip” joint. Experiments demonstrate that the resulting mechanism can deliver more than half again as much kinetic energy to the body (or more than double the kinetic energy if the full workspace is used), and offers a five-fold increase in energy storage and collision efficiency relative to the conventional design.

We develop a stochastic framework for modeling and analysis of robot navigation in the presence of obstacles. We show that, with appropriate assumptions, the probability of a robot avoiding a given obstacle can be reduced to a function of a single dimensionless parameter which captures all relevant quantities of the problem. This parameter is analogous to the Péclet number considered in the literature on mass transport in advection-diffusion fluid flows. Using the framework we also compute statistics of the time required to escape an obstacle in an informative case. The results of the computation show that adding noise to the navigation strategy can improve performance. Finally, we present experimental results that illustrate these performance improvements on a robotic platform.

We consider the problem of visually servoing a legged vehicle with unicycle-like nonholonomic constraints subject to second-order fore-aft dynamics in its horizontal-plane. We target applications to rugged environments characterized by complex terrain likely to significantly perturb the robot's nominal dynamics. At the same time, it is crucial that the camera avoid “obstacle” poses where absolute localization would be compromised by even partial loss of landmark visibility. Hence, we seek a controller whose robustness against disturbances and obstacle avoidance capabilities can be assured by a strict global Lyapunov function. Since the nonholonomic constraints preclude smooth point stabilizability we introduce an extra degree of sensory freedom, affixing the camera to an actuated panning axis on the robot's back. Smooth stabilizability to the robot-orientation-indifferent goal cycle no longer precluded, we construct a controller and strict global Lyapunov function with the desired properties. We implement several versions of the scheme on a RHex robot maneuvering over slippery ground and document its successful empirical performance.

This paper addresses the coordinated navigation of multiple independently actuated disk-shaped robots-all placed within the same disk-shaped workspace. Assuming perfect sensing, shared-centralized communications and computation, as well as perfect actuation, we encode complete information about the goal, obstacles, and workspace boundary using an artificial potential function over the configuration space of the robots' simultaneous nonoverlapping positions. The closed-loop dynamics governing the motion of each (velocity-controlled) robot take the form of the appropriate projection of the gradient of this function. We impose (conservative) restrictions on the allowable goal positions that yield sufficient conditions for convergence: We prove that this construction is an essential navigation function that guarantees collision-free motion of each robot to its destination from almost all initial free placements. The results of an extensive simulation study investigate practical issues such as average resulting trajectory length and robustness against simulated sensor noise.

We propose a new paradigm for reactive wall-following by a planar robot taking the form of an actively steered sensor model that augments the robot's motion dynamics. We postulate a foveated sensor capable of delivering third-order infinitesimal (range, tangent, and curvature) data at a point along a wall (modeled as an unknown smooth plane curve) specified by the angle of the ray from the robot's body that first intersects it. We develop feedback policies for the coupled (point or unicycle) sensorimotor system that drive the sensor's foveal angle as a function of the instantaneous infinitesimal data, in accord with the trade-off between a desired standoff and progress-rate as the wall's curvature varies unpredictably in the manner of an unmodeled noise signal. We prove that in any neighborhood within which the third-order infinitesimal data accurately predicts the local “shape” of the wall, neither robot will ever hit it. We empirically demonstrate with comparative physical studies that the new active sensor management strategy yields superior average tracking performance and avoids catastrophic collisions or wall losses relative to the passive sensor variant.

As dynamic robot behaviors become more capable and well understood, the need arises for a wide variety of equally capable and systematically applicable transitions between them. We use a hybrid systems framework to characterize the dynamic transitions of a planar “legged” rigid body from rest on level ground to a fully aerial state. The various contact conditions fit together to form a topologically regular structure, the “ground reaction complex”. The body's actuated dynamics excite multifarious transitions between the cells of this complex, whose regular adjacency relations index naturally the resulting “leaps” (path sequences through the cells from rest to free flight). We exhibit on a RHex robot some of the most interesting “words” formed by these achievable path sequences, documenting unprecedented levels of performance and new application possibilities that illustrate the value of understanding and expressing this vocabulary systematically.

On challenging, uneven terrain a legged robot's open loop posture will almost inevitably be inefficient, due to uncoordinated support of gravitational loads with coupled internal torques. By reasoning about certain structural properties governing the infinitesimal kinematics of the closed chains arising from a typical stance, we have developed a computationally trivial self-manipulation behavior that can minimize both internal and external torques absent any terrain information. The key to this behavior is a change of basis in torque space that approximates the partially decoupled nature of the two types of disturbances. The new coordinates reveal how to use actuator current measurements as proprioceptive sensors for the approximate gradients of both the internal and external task potential fields, without recourse to further modeling. The behavior is derived using a manipulation framework informed by the dual relationship between a legged robot and a multifingered hand. We implement the reactive posture controller resulting from simple online descent along these proprioceptively sensed gradients on the X-RHex robot to document the significant savings in standing power.

Biomechanical studies suggest that animals' abilities to tune their effective leg compliance in response to changing terrain conditions plays an important role in their agile, robust locomotion. However, despite growing interest in leg compliance within the robotics literature, little experimental work has been reported on tunable passive leg compliance in running machines. In this paper we present an empirical study into the role of leg compliance using a composite tunable leg design implemented on our dynamic hexapod, EduBot, with gaits optimized for running speed using a range of leg stiffnesses, on two different surface stiffnesses, and with two different payload configurations (0 kg and 0.91 kg). We found that leg stiffness, surface compliance, and payload had a significant impact on the robot's final optimized speed and efficiency. These results document the value and efficacy of what we believe is the first autonomous dynamic legged robot capable of runtime leg stiffness adjustment.

We present a framework for detecting, identifying, and recovering within stride from faults and other leg contact disturbances encountered by a walking hexapedal robot. Detection is achieved by means of a software contact-event sensor with no additional sensing hardware beyond the commercial actuators' standard shaft encoders. A simple finite state machine identifies disturbances as due either to an expected ground contact, a missing ground contact indicating leg fault, or an unexpected “wall” contact. Recovery proceeds as necessary by means of a recently developed topological gait transition coordinator. We demonstrate the efficacy of this system by presenting preliminary data arising from two reactive behaviors - wall avoidance and leg-break recovery. We believe that extensions of this framework will enable reactive behaviors allowing the robot to function with guarded autonomy under widely varying terrain and self-health conditions.

This paper describes the development of a legged robot designed for general locomotion of complex terrain but specialized for dynamical, high-speed climbing of a uniformly convex cylindrical structure, such as an outdoor telephone pole. This robot, the RiSE V3 climbing machine-mass 5.4 kg, length 70 cm, excluding a 28 cm tail appendage-includes several novel mechanical features, including novel linkage designs for its legs and a non-backdrivable, energy-dense power transmission to enable high-speed climbing. We summarize the robot's design and document a climbing behavior that achieves rapid ascent of a wooden telephone pole at 21 cm/s, a speed previously unachieved-and, we believe, heretofore impossible-with a robot of this scale. The behavioral gait of the robot employs the mechanical design to propel the body forward while passively maintaining yaw, pitch, and roll stability during climbing locomotion. The robot's general-purpose legged design coupled with its specialized ability to quickly gain elevation and park at a vertical station silently with minimal energy consumption suggest potential applications including search and surveillance operations as well as ad hoc networking.

Traditional legged runners and climbers have relied heavily on gait generators in the form of internal clocks or reference trajectories. In contrast, here we present physical experiments with a fast, dynamical, vertical wall climbing robot accompanying a stability proof for the controller that generates it without any need for an additional internal clock or reference signal. Specifically, we show that this ¿self-exciting¿ controller does indeed generate an ¿almost¿ globally asymptotically stable limit cycle: the attractor basin is as large as topologically possible and includes all the state space excluding a set with empty interior. We offer an empirical comparison of the resulting climbing behavior to that achieved by a more conventional clock-generated gait trajectory tracker. The new, self-exciting gait generator exhibits a marked improvement in vertical climbing speed, in fact setting a new benchmark in dynamic climbing by achieving a vertical speed of 1.5 body lengths per second.

Legged robots are by nature strongly non-linear, high-dimensional systems whose full complexity permits neither tractable mathematical analysis nor comprehensive numerical study. In consequence, a growing body of literature interrogates simplified "template" (Full and Koditschek, 1999; Ghigliazza et al., 2005) models - to date almost exclusively confined to sagittal- or horizontal-plane motion - with the aim of gaining insight into the design or control of the far messier reality. In this paper we introduce a simple bounding-in-place ("BIP") model as a candidate frontal plane template for straight-ahead level ground running and explore its use in formulating hypotheses about whether and why rolling motion is important in legged locomotion. Numerical study of left-right compliance asymmetry in the BIP model suggests that compliance ratios yielding lowest steady state roll suffer far longer disturbance recovery transients than those promoting greater steady state roll. We offer preliminary experimental data obtained from video motion capture data of the frontal plane disturbance recovery patterns of a RHex-like hexapod suggesting a correspondence to the conclusions of the numerical study.

We report on a hybrid 12-dimensional full body state estimator for a hexapod robot executing a jogging gait in steady state on level terrain with regularly alternating ground contact and aerial phases of motion. We use a repeating sequence of continuous time dynamical models that are switched in and out of an extended Kalman filter to fuse measurements from a novel leg pose sensor and inertial sensors. Our inertial measurement unit supplements the traditionally paired three-axis rate gyro and three-axis accelerometer with a set of three additional three-axis accelerometer suites, thereby providing additional angular acceleration measurement, avoiding the need for localization of the accelerometer at the center of mass on the robot's body, and simplifying installation and calibration. We implement this estimation procedure offline, using data extracted from numerous repeated runs of the hexapod robot RHex (bearing the appropriate sensor suite) and evaluate its performance with reference to a visual ground-truth measurement system, comparing as well the relative performance of different fusion approaches implemented via different model sequences

We report on progress toward a continuous time full 6 DOF translational body state estimator for a hexapod robot executing a jogging gait (with 4 consecutive phases: tripod stance, liftoff transient, aerial, and touchdown transient) on level ground. We use a sequence of dynamical models imported into a standard Kalman Filter to fuse measurements from a novel leg pose sensor and a conventional inertial measurement unit. We implement this estimation procedure on the hexapod robot RHex and evaluate its performance using a visual ground truth measurement system. We also compare the relative performance of different fusion approaches implemented via different model sequences.

We report on a continuous-time rigid-body pose estimator for a walking hexapod robot. Assuming at least three legs remain in ground contact at all times, our algorithm uses the outputs of six leg-configuration sensor models together with a priori knowledge of the ground and robot kinematics to compute instantaneous estimates of the 6-degrees-of-freedom (6-DOF) body pose. We implement this estimation procedure on the robot RHex by means of a novel sensory system incorporating a model relating compliant leg member strain to leg configuration delivered to the onboard CPU over a customized cheap high-performance local wireless network. We evaluate the performance of this algorithm at widely varying body speeds and over dramatically different ground conditions by means of a 6-DOF vision-based ground-truth measurement system (GTMS). We also compare the odometry performance to that of sensorless schemes - both legged as well as on a wheeled version of the robot - using GTMS measurements of elapsed distance.

Gait parameter adaptation on a physical robot is an error-prone, tedious and time-consuming process. In this paper we present a system for gait adaptation in our RHex series of hexapedal robots that renders this arduous process nearly autonomous. The robot adapts its gait parameters by recourse to a modified version of Nelder-Mead descent, while managing its self-experiments and measuring the outcome by visual servoing within a partially engineered environment The resulting performance gains extend considerably beyond what we have managed with hand tuning. For example, the best hand tuned alternating tripod gaits never exceeded 0.8 m/s nor achieved specific resistance below 2.0. In contrast, Nelder-Mead based tuning has yielded alternating tripod gaits at 2.7 m/s (well over 5 body lengths per second) and reduced specific resistance to 0.6 while requiring little human intervention at low and moderate speeds. Comparable gains have been achieved on the much larger ruggedized version of this machine.

We report on a continuous time full body state estimator for a hexapod robot operating in the dynamical regime (entailing a significant aerial phase) on level ground that combines a conventional rate gyro with a novel leg strain based body pose estimator. We implement this estimation procedure on the robot RHex and evaluate its performance using a visual ground truth measurement system. As an independent assessment of our estimator's quality we also compare its odometry performance to sensorless averaged open loop distance-per-stride estimates.

This paper addresses problems of robot navigation with nonholonomic motion constraints and perceptual cues arising from onboard visual servoing in partially engineered environments. We focus on a unicycle motion model and a variety of artificial beacon constellations motivated by relevance to the autonomous hexapod, RHex. We propose a general hybrid procedure that adapts to the constrained motion setting the standard feedback controller arising from a navigation function in the fully actuated case by switching back and forth between moving "down" and "across" the associated gradient field toward the stable manifold it induces in the constrained dynamics. Guaranteed to avoid obstacles in all cases, we provide some reasonably general sufficient conditions under which the new procedure guarantees convergence to the goal. Simulations are provided for perceptual models previously introduced by other authors.

A collection of unactuated disk-shaped "parts" must be brought by an actuated manipulator robot into a specified configuration from arbitrary initial conditions. The task is cast as a noncooperative game played among the parts-which in turn yields a feedback-based event-driven approach to plan generation and execution. The correctness of this approach, an open question, has been demonstrated in simpler settings and is further suggested by the extensive experiments reported here using an actual working implementation with EDAR-a mobile robot operating in a purely feedback-based event-driven manner. These results verify the reliability of this approach against uncertainties in sensory information and unanticipated changes in workspace configuration.

In this paper, we report on a new stability analysis for hybrid legged locomotion systems based on factorization of return maps. We apply this analysis to a family of models of the spring loaded inverted pendulum (SLIP) with different leg recirculation strategies. We obtain a necessary condition for the asymptotic stability of those models, which is formulated as an exact algebraic expression despite the non-integrability of the SLIP dynamics. We outline the application of this analysis of other models of legged locomotion and it importance for the stability of legged robots and animals.

We report on a novel leg strain sensory system for the autonomous robot RHex [Saranli U. et al., 2001] implemented upon a cheap, high performance local wireless network [H. Komsuoglu, 2002]. We introduce a model for RHex's 4-bar legs [E.Z. Moore, 2001] relating leg strain to leg kinematic configuration in the body coordinate frame. We compare against ground truth measurement the performance of the model operating on real-time leg strain data generated under completely realistic operating conditions. We introduce an algorithm for computing six degree of freedom body posture measurements in world frame coordinates from the outputs of the six leg configuration models, together with a priori information about the ground. We discuss the manner in which such stance phase configuration estimates will be fused with other sensory data to develop the continuous time full body state estimates for RHex.

This paper addresses the problem of registering the hexapedal robot, RHex, relative to a known set of beacons, by real-time visual servoing. A suitably constructed navigation function represents the task, in the sense that for a completely actuated machine in the horizontal plane, the gradient dynamics guarantee convergence to the visually cued goal without ever losing sight of the beacons that define it. Since the horizontal plane behavior of RHex can be represented as a unicycle, feeding back the navigation function gradient avoids loss of beacons, but does not yield an asymptotically stable goal. We address new problems arising from the configuration of the beacons and present preliminary experimental results that illustrate the discrepancies between the idealized and physical robot actuation capabilities.

In this paper, we introduce a hexapedal locomotion controller that simulation evidence suggests will be capable of driving our RHex robot at speeds exceeding five body lengths per second with reliable stability and rapid maneuverability. We use a low dimensional passively compliant biped as a "template" - a control target for the alternating tripod gait of the physical machine. We impose upon the physical machine an approximate inverse dynamics within-stride controller designed to force the true high dimensional system dynamics down onto the lower dimensional subspace corresponding to the template. Numerical simulations suggest the presence of asymptotically stable running gaits with large basins of attraction. Moreover, this controller improves substantially the maneuverability and dynamic range of RHex's running behaviors relative to the initial prototype open-loop algorithms.

We report on the design and analysis of a controller which can achieve dynamical self-righting of our hexapedal robot, RHex. We present an empirically developed control procedure which works reasonably well on indoor surfaces, using a hybrid energy pumping strategy to overcome torque limitations of its actuators. Subsequent modeling and analysis yields a new controller with a much wider domain of success as well as a preliminary understanding of the necessary hybrid control strategy. Simulation results demonstrate the superiority of the improved control strategy to the first generation empirically designed controller.

This paper presents a framework for visual servoing that guarantees convergence to a visible goal from almost every initially visible configurations while maintaining full view of all the feature points along the way. The method applies to first- and second-order fully actuated plant models. The solution entails three components: a model for the "occlusion-free" configurations; a change of coordinates from image to model coordinates; and a navigation function for the model space. We present three example applications of the framework, along with experimental validation of its practical efficacy.

We describe a method for the decentralized phase regulation of two coupled hybrid oscillators. In particular, we prove that the application of this synchronization method to two hopping robots, each of which individually achieves only asymptotically stable hopping, results in an asymptotically stable limit cycle for the coupled system exhibiting the desired phase difference. This extends our previous work wherein the application of the method to two individually deadbeat-stabilized oscillators (paddle juggling mechanisms) was shown to yield the desired result. Central to this method is the idea that cyclic systems may be composed into a larger, aggregate, cyclic system. Its application entails moving from physical coordinates (for example, the position and velocity of each constituent mechanism) to the coordinates of phase and phase velocity. Within this canonical coordinate system we construct a model dynamical system, called a reference field, which encodes the desired behavior of each cyclic system as well as the phase relationships between them. We then force the actual composite system to behave like the model.

We report on our progress in extending the behavioral repertoire of RHex, a compliant leg hexapod robot. We introduce two new controllers, one for climbing constant slope inclinations and one for achieving higher speeds via pronking, a gait that incorporates a, substantial aerial phase. In both cases, we make use of an underlying open-loop control strategy, combined with low bandwidth feedback to modulate its parameters. The inclination behavior arises from our initial alternating tripod walking controller and adjusts the angle offsets of individual leg motion profiles based on inertial sensing of the average surface slope. Similarly, the pronking controller makes use of a "virtual" leg touchdown sensing mechanism to adjust the frequency of the open-loop pronking, effectively synchronizing the controller with the natural oscillations of the mechanical system. Experimental results demonstrate good performance on slopes inclined up to /spl sim/250 and pronking up to speeds approaching 2 body lengths per second (/spl sim/1.0 m/s).

This paper deals with the parts moving problem based on an event-driven planning and control. We are interested in developing feedback based approaches to the automatic generation of actuator commands that cause the robot to move a set of parts from an arbitrary initial disassembled configuration to a specified final configuration. In the Phase 1 of this project, a composite algorithm that reactively switches between different feedback controllers is shown to induce a noncooperative game being played among the parts being manipulated. This paper describes experimental results with EDAR (event-driven assembler robot) developed for moving parts based on feedback techniques.

We introduce tools which help one to compose concurrent, hybrid control programs for a class of distributed robotic systems, assuming a palette of controllers for individual tasks is already constructed. These tools, which combine the backchaining of continuous robot behaviors with Petri nets, expand on successful work in sequential composition of robot behaviors. We apply these ideas to the design and verification of a robotic bucket brigade and to simple, distributed assembly tasks as found in automated factories.

We present the design, modeling and preliminary control of RHex, an autonomous dynamically stable hexapod possessing merely six actuated degrees of freedom (at the hip attachment of each leg). Our design emphasizes mechanical simplicity as well as power and computational autonomy, critical components for legged robotics applications. A compliant hexapod model, used to build a simulation environment closely informed the design and construction of the physical machine and promises to inform, similarly, our future analysis as well. Simulations and experiments show that RHex can achieve dynamically stable walking, running and turning with very simple clock driven open-loop control strategies.

The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for "learning" piecewise linear scalar functions in two settings: "approximation", where an "oracle" outputs accurate functional values in response to input queries; and "estimation", where only a fixed discrete data base of input-output pairs is available. We provide a local convergence result for the approximation version of the GI algorithm as well as a study of its numerical performance in the estimation setting. We conclude that PLH offers accuracy closed to that of a neural net while requiring, via our GI algorithm, far shorter training time and preserving desired invariant properties unlike any other presently popular basis family.

We report on our empirical studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an ape's brachiation, we encode this task as the output of a "target dynamical system". Numerical simulations indicate that the resulting controller solves a number of brachiation problems that we term the "ladder", "swing-up", and "rope" problems. Preliminary analysis provides some explanation for this success. The proposed controller is implemented on a physical system in our laboratory. The robot achieves behaviors including "swing locomotion" and "swing up" and is capable of continuous locomotion over several rungs of a ladder. We discuss a number of formal questions whose answers will be required to gain a full understanding of the strengths and weaknesses of this approach.

We describe a hybrid planar image-based servo algorithm which, for a simplified planar convex rigid body, converges to a static goal for all initial conditions within the workspace of the camera. This is achieved by using the sequential composition of a palette of continuous image based controllers. Each sub-controller, based on a specified set of collinear feature points, is shown to converge for all initial configurations in which the feature points are visible. Furthermore, the controller guarantees that the body will maintain a "visible" orientation, i.e. the feature points will always be in view of the camera. This is achieved by introducing a change of coordinates from SE(2) to an image plane measurement of three points, and imposing a navigation function in that coordinate system. Our intuition suggests that appropriately generalized versions of these ideas may be extended to SE(3).

We have previously developed a brachiation controller that allows a two degree of freedom robot to swing from hand-hold to hand-hold on a horizontal ladder with evenly space rungs as well as swing up from a suspended posture using a "target dynamics" controller. In this paper, we extend this class of algorithms to handle the much more natural problem of locomotion over irregularly spaced hand-holds. Numerical simulations and laboratory experiments illustrate the effectiveness of this generalization.

We describe work-in-progress toward a nonlinear image-based rigid body dynamic triangulator which we believe tracks a moving target from "essentially all" initial conditions (all initial conditions except a set of measure zero). The dynamic triangulator depends on the goal state only through its image plane position and velocity and requires a navigation function, imposed directly upon image features, to serve as a regressor for a gradient-like state update law.

We report on our recent empirical success in the study of a two-link brachiating robot. The "target dynamics" controller developed in our previous work (1997) is implemented on a physical system in our laboratory. The swing locomotion and swing-up behavior of the robot as well as continuous locomotion have been successfully attained. The experimental results illustrate the effectiveness of our control strategy.

We propose a new family of controllers for multi-jointed planar monoped runners, based on approximate but accurate models of the stance phase dynamics of a two degree of freedom "SLIP" leg. Unlike previous approaches, the new scheme gives control over all parameters of the system including the hopping height, forward speed and duty cycle. The control laws are "deadbeat" in nature, derived by computing the inverse of an approximate return map and corrected by integral compensation. We use the expressions obtained in this way to control the original SLIP leg as well as radically different, more realistic four degree of freedom legs. In each case, the performance of the deadbeat scheme in controlling forward running velocity is compared to a modified Raibert control strategy, whose experimental stability properties have been analyzed carefully in the low degree of freedom setting.

We report on our preliminary studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an ape's brachiation, we encode this task as the output of a "target dynamical system". Numerical simulations indicate that the resulting controller solves a number of brachiating problems that we term the "ladder", "swing up" and "rope" problems. Preliminary analysis provides some explanation for this success. We discuss a number of formal questions whose answers will be required to gain a full understanding of the strengths and weaknesses of this approach.

We characterize equilibrium gaits of a small knee monoped in terms of manifest parameters by recourse to approximate closed form expressions. We first eliminate gravity during stance and choose a very special model of potential energy storage in the knee. Next, we introduce simple closed form approximations, motivated by the mean value theorem, to the elliptic integrals arising in the more general case. In so doing, we derive a conjectured generalization applicable to small knee monopeds with an arbitrary knee potential. Finally, we introduce a new closed form perturbation intended to adjust the approximate coordinate transformations to the presence of gravity. Simulation data is offered as evidence for the efficacy (to within roughly 5-10% accuracy) of both the proposed generalization across knee potentials and the proposed perturbation for the presence of gravity during stance.

We present a system for generation and recognition of oscillatory gestures. Inspired by gestures used in two representative human-to-human control areas, we consider a set of oscillatory motions and refine from them a 24 gesture lexicon. Each gesture is modeled as a dynamical system with added geometric constraints to allow for real time gesture recognition using a small amount of processing time and memory. The gestures are used to control a pan-tilt camera neck. We propose extensions for use in areas such as mobile robot control and telerobotics.

We present a working implementation of a dynamics based architecture for visual sensing. This architecture provides field rate estimates of the positions and velocities of two independent falling balls in the face of repeated visual occlusions and departures from the field of view. The practical success of this system can be attributed to the interconnection of two strongly nonlinear dynamical systems: a novel triangulating state estimator; and an image plane window controller. We detail the architecture of this active sensor, provide data documenting its performance, and offer an analysis of its soundness in the form of a convergence proof for the estimator and a boundedness proof for the controller.

A simplified lossless model of the Raibert planar hopper is introduced for the purpose of analytically studying the control of forward velocity. A closed-form return map describing the robot's state at the next hop as a function of that at the current hop is derived. The Raibert forward velocity controller is introduced and the fixed points of the closed loop system are characterized as well as the stability of these points. A new control law inspired by this analysis is introduced and compared with the Raibert control law.

In this paper we demonstrate that a passive vibration strategy can bring a 1 degree of freedom ball to a known trajectory from all possible initial configurations. We draw motivation from the problem of parts feeding in sensorless assembly. We provide simulation results suggesting the relevance of our analytical results to the parts feeding problem.

We report on our initial efforts to build robot feedback controllers that develop increased capability from simpler constituent controllers. Previous work with our three degree of freedom robot has resulted in a machine that exhibits various dynamically dexterous skills of superlative ability but very narrow behavioral scope. We focus here on the development of both a formalism and practice for the composition of constituent controllers. The composite should yield automatically purposive combinations of these skills that reach goals no one of the defining controllers could have achieved in isolation. The specific task we initially target, the "dynamical pick and place", requires the robot to acquire balls that have been "randomly" thrown into its work space and set them safely at rest in a specified location. We present a brief overview of the constituent behaviors and a mechanism for their combination along with documentation of our preliminary empirical successes.

This paper describes a simple visual servoing control algorithm capable of robustly positioning a three degree of freedom end effector based only on information from a stereo vision system. The proposed control algorithm does not require estimates of the gripper's spatial position, a significant source of calibration sensitivity. The controller is completely immune to positional camera calibration errors, and we demonstrate robustness to orientation miscalibration through a series of simulations and experiments.

In previous papers we have reported successful laboratory implementations of a family of juggling algorithms. In all but the one degree of freedom case, these empirically successful algorithms have so far resisted our analytical efforts to explain why they work. This is in large measure a consequence of our inability to write down using elementary functions an expression for the closed loop dynamics they induce. We discuss in this paper a modified juggling algorithm whose resulting closed loop dynamics can be written down directly. We offer data establishing the empirical success of the new algorithm. Theoretical analysis of the closed loop dynamics is presently in progress.>

In the recent successful effort to achieve the spatial two-juggle - batting two freely falling balls into independent stable periodic vertical orbits by repeated impacts with a three degree of freedom robot arm, the authors have found it necessary to introduce a dynamical window manager into their real-time stereo vision. This paper describes these necessary enhancements to the original vision system and then proposes a more formal account of how such a feedback based sensor might be understood to work. Further experimentation will be required to determine the extent to which the analytical model explains (and might thus be used as a tool to improve) the performance of the system presently working in the laboratory.

A model-based adaptive controller and proof of its global asymptotic stability with respect to the standard rigid-body model of robot-arm dynamics are presented. Experimental data from a study of one new and several established globally asymptotically stable adaptive controllers on two very different robot arms: (1) demonstrate the superior tracking performance afforded by the model-based algorithms over conventional PD control; (2) demonstrate and compare the superior performance of adaptive model-based algorithms over their nonadaptive counterparts; (3) reconcile several previous contrasting empirical studies; and (4) examine contexts that compromise their advantage.>

The authors review their progress to date in eliciting dynamically dexterous behaviors from a 3-d.o.f. direct drive robot manipulator whose real-time stereo cameras provide 60 Hz sampled images of multiple freely falling bodies in highly structured lighting conditions. At present, the robot is capable of forcing a single ping-pong ball into a specified steady-state (near) periodic vertical motion by repeated controlled impacts with a rigid paddle. The robot sustains the steady-state behavior over long periods (typically many thousands of impacts) and is capable of recovering from significant unexpected adversarial perturbations of the ball's flight phase. Gain tuning experiments corroborate the authors' contention that the stability mechanism underlying the robot's reliability can be attributed to the same nonlinear dynamics responsible for analogous behavior in a previous 1-d.o.f. robot.>

An approach to the problem of controlling automated assembly tasks using artificial potential functions is described. The authors address the automatic generation of actuator commands for a robot manipulator that result in the motion of a collection of rigid-body parts from disassembled initial configurations to an assembled final configuration. A simple class of tasks, 2D sphere assemblies, is examined. A primitive constructive theory for the control of this class of tasks is presented. Preliminary computer simulations demonstrate that the proposed approach may provide surprisingly good performance.>

A methodology for exact robot motion planning and control that unifies the purely kinematic path planning problem with the lower level feedback controller design is presented. Complete information about a freespace and goal is encoded in the form of a special artificial potential function, called a navigation function, that connects the kinematic planning problem with the dynamic execution problem in a provably correct fashion. The navigation function automatically gives rise to a bounded-torque feedback controller for the robot's actuators that guarantees collision-free motion and convergence to the destination from almost all initial free configurations. A formula for navigation functions that guide a point-mass robot in a generalized sphere world is developed. The simplest member of this family is a space obtained by puncturing a disk by an arbitrary number of smaller disjoint disks representing obstacles. The other spaces are obtained from this model by a suitable coordinate transformation. Simulation results for planar scenarios are provided.>

An adaptive controller is discussed and a proof of its global asymptotic stability with respect to the standard rigid body model of robot arm dynamics is presented. Experimental data from a study of this and other globally asymptotically stable adaptive controllers on two very different robot arms are used to reconcile several previous contrasting empirical studies, demonstrate and compare their superior tracking performance, and examine contexts that compromise their advantage.>

An approach to the problem of automated assembly planning and control using artificial potential functions is described. A simple class of tasks, 2D sphere assemblies, is examined. A constructive theory for the planning and control of this class of tasks is presented. Computer simulations demonstrate that the approach may provide surprisingly good performance.>

Recent results of dynamical systems theory are used to derive strong predictions concerning the global properties of a simplified model of a planar juggling robot. In particular, it is found that certain lower-order local (linearized) stability properties determine the essential global (nonlinear) stability properties, and that successive increments in the controller gain settings give rise to a cascade of stable period-doubling bifurcations that comprise a universal route to chaos. The theoretical predictions are verified by simulation and corroborated by experimental data from the juggling robot.>

Navigation functions on forests of stars, geometrically complicated C-spaces (configuration spaces) that are topologically indistinguishable from a simple disc punctured by disjoint smaller discs representing model obstacles, are constructed. For reasons of mathematical tractability, each C-space obstacle is approximated by a Boolean combination of linear and quadratic polynomial inequalities (with sharp corners allowed), and a calculus of implicit representations is used to effectively represent such obstacles. Evidence is provided of the effectiveness of this technology of implicit representations in the form of several simulation studies.>

The performance of real-time distributed control systems is shown to depend critically on both communication and computation costs. A taxonomy for distributed system performance measurement is introduced. A roughly accurate method of performance prediction for simple systems is presented. Experimental results demonstrate the effects of communication protocols on real-world system performance.>

A formalism is developed for describing and analyzing a very simple representation of a class of robotic tasks which require dynamical dexterity, among them the task of juggling. Empirical success has been achieved with a class of control algorithms for this task domain, called mirror algorithms. Using the formalism for representing the task domain, and encoding within it the desired robot behavior, it can be proven that a suitable mirror algorithm is correct with respect to a special task. Although the generation of algorithm geometry is completely heuristic at present, the analytical tractability of the resulting robot-environment closed loop, which is demonstrated, raises the hope that sufficient understanding may soon be realized to afford automatic translation of suitably expressed task definitions into provable correct empirically valid robot controller designs.>

The authors consider the construction of navigation functions on configuration spaces whose geometric expressiveness is rich enough for navigation amidst real-world obstacles. They describe a general methodology which extends the construction of navigation functions on sphere worlds to any smoothly deformable space. According to this methodology, the problem of constructing a navigation function is reduced to the construction of a transformation mapping a given space into its model sphere world. The transformation must satisfy certain regularity conditions guaranteeing invariance of the navigation function properties. The authors demonstrate this idea by constructing navigation functions on star worlds: n-dimensional star shaped subsets of E/sup n/ punctured by any finite number of smaller disjoint n-dimensional stars. This construction yields automatically a bounded torque feedback control law which is guaranteed to guide the robot to destination point from almost every initial position without hitting any obstacle.>

The authors construct a simplified model of a dynamically dexterous robot, M.H. Raibert's hopper, and investigate its elegant, physically based control strategies. Analysis of induced discrete dynamics leads to strong conclusions concerning global limiting properties. These conclusions are then verified by computer simulation of the simplified models, the correspondence of which to the true physical apparatus is seen to be acceptable as well.>

The utility of artificial potential functions is explored as a means of translating automatically a robot task description into a feedback control law to drive the robot actuators. A class of functions is sought which will guide a point robot amid any finite number of spherically bounded obstacles in Euclidean n-space toward an arbitrary destination point. By introducing a set of additional constraints, the subclass of navigation functions is defined. This class is dynamically sound in the sense that the actual mechanical system will inherit the essential aspects of the qualitative behavior of the gradient lines of the cost function. An existence proof is given by constructing a one parameter family of such functions; the parameter is used to guarantee the absence of local minima.>

The limits in global navigation capability of potential function based robot control algorithms are explored. Elementary tools of algebraic and differential topology are used to advance arguments suggesting the existence of potential functions over a bounded planar region with arbitrary fixed obstacles possessed of a unique local minimum. A class of such potential functions is constructed for certain cases of a planar disk region with an arbitrary number of smaller disks removed.

The concept of an automaton operating in a multi-teacher environment is introduced, and several interesting questions that arise in this context are examined. In particular, we concentrate on the consequences of adding a new teacher to an existing n-teacher set as it affects the choice of a switching strategy. The effect of this choice on expediency and speed of convergence is presented for a specific automaton structure.