A new stabilizing nonlinear controller for the vertical motion of an electrically actuated hopping robot is introduced and analyzed. The approach starts by finding reference limit cycles from the "passive dynamics" of a mass-spring system. The controller then modulates the system dynamics via the leg actuator during the stance phase to force the system trajectory to converge to this reference limit cycle. The controlled system dynamics is a continuous yet nonsmooth vector field. A piecewise-continuous Lyapunov function and the general forms of Lasalle's invariance and domain of attraction theorems are used to prove global asymptotic stability of the desired limit cycles. It is also shown that the derived passive dynamic cycles are indeed the positive limit sets of the controlled system. The rate of convergence can be adjusted but is limited by actuator constraints.

This paper presents experiments with a new, three-dimensional bipedal running behaviour for our robotic hexapod, RHex. The robot and the bipedal gait are underactuated, using only one actuated degree of freedom per compliant leg. We doubled up RHex's hind legs by attaching a duplicate set of hind legs at 180deg, forming 'S' shaped legs. This reduces the actuator speed requirements during non-contact, while preserving the bipedal dynamics and control challenges. Stable running at average speeds between 0.67 and 1.07 m/s with a success rate of 100% over thirty runs is obtained with only leg angle and body orientation feedback

This paper presents the expansion and implementation of the controlled passive dynamic running (CPDR) strategy for legged robots, previously presented by the authors. The CPDR exploits the underlying passive dynamic operation of the robot's mechanical systems to reduce the energy spent for locomotion. Meanwhile, it ensures the stability of the vertical and forward motions as the robot speed varies. An "adaptive energy controller" stabilizes the hopping height accurately over a range of operating conditions. The passive dynamic derivations for the Monopod, together with the foot-placement algorithm and model-based joint controllers, are used to control the forward speed about the passive operation trajectories. New locomotion variables are used for robust synchronization between the hip-body and the leg oscillations. ARL-Monopod II achieved a speed of 1.25 m/s with specific resistance (a measure for energy cost of locomotion) of 30% of the earlier robot ARL-Monopod I, its predecessor, due to the newer hip and leg design and application of the CPDR control strategy

In this paper the authors discuss control and modeling issues significant for constructing simple running controllers and building experimentally validated simulation models for dynamically stable robots. A bounding controller resulting in dynamically stable running up to 1.3 m/s for the Scout II quadruped is presented. Simulation models are built and compared with experimental data to test the viability of various simplifying assumptions common in the literature for running robots. The authors demonstrate the need for including motor saturation and nor rigid torque transmission characteristics into simulation models. Similar issues are likely to be important in other legged robots as well. An extensive suite of experimental results documents the robot's performance and validates simulation models.

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.

This paper describes an underwater walking robotic system being developed under the name AQUA, the goals of the AQUA project, the overall hardware and software design, the basic hardware and sensor packages that have been developed, and some initial experiments. The robot is based on the RHex hexapod robot and uses a suite of sensing technologies, primarily based on computer vision and INS, to allow it to navigate and map clear shallow-water environments. The sensor-based navigation and mapping algorithms are based on the use of both artificial floating visual and acoustic landmarks as well as on naturally occurring underwater landmarks and trinocular stereo.

Animal legs are much more complex than necessary for running on horizontal surfaces. Past research shows that, despite their complexity, they act essentially like simple pogo sticks, or the "spring loaded inverted pendulum" (SLIP). In this paper, the possibility of the realization of a SLIP model using a spring in the leg and only one actuator at the hip is investigated first in numerical simulation and then in experiments. A simple controller results in running at 0.80 m/s (6.7 leg lengths per second). The stability and robustness of the resulting motion is demonstrated.

We present the first controller that allows our small hexapod robot, RHex, to descend a wide variety of regular sized, "real world" stairs. After selecting one of two sets of trajectories, depending on the slope of the stairs, our open-loop, clock-driven controllers require no further operator input nor task level feedback. Energetics for stair descent is captured via specific resistance values and compared to stair ascent and other behaviors. Even though the algorithms developed and validated in this paper were developed for a particular robot, the basic motion strategies, and the phase relationships between the contralateral leg pairs are likely applicable to other hexapod robots of similar size as well.

We describe a model predicting the output torque of the battery-amplifier-actuator-gear combination used on the hexapod robot RHex, based on requested PWM (pulse width modulation) duty cycle to the amplifier, battery voltage, and motor speed. The model is broken into independent components, each experimentally validated: power source (battery), motor amplifier, motor and (planetary) gear. The resulting aggregate model shows <6% full scale RMS error in predicting output torque in the first quadrant of operation (positive torques). Understanding the key ingredients and the attainable accuracies of torque production models in our commonly used battery-amplifier-actuator-gear combinations is critical for mobile robots, in order to minimize sensing, and thus space, size, weight, power consumption, failure rate, and cost of mobile robots.

In this paper, we study the passive dynamics of quadrupedal bounding, based on a simplified model of our Scout II quadruped robot. Surprisingly, numerical return map studies reveal that passive generation of a large variety of cyclic bounding motion is possible. Most strikingly, local stability analysis shows that the dynamics of the open loop passive system alone can confer stability of the motion. Stability improves at higher speeds, which is in agreement with recent results from biomechanics. These results can be used in developing a general control methodology for legged robots, resulting from the synthesis of feed-forward and feedback models that take advantage of the mechanical system, and might explain the success of simple, open loop bounding controllers on our experimental robot.

RHex is a hexapod with compliant legs and only six actuated degrees of freedom. Its ability to traverse highly fractured and unstable terrain, as well ascend and descend a particular flight of stairs has already been documented. In this paper, we describe an open loop controller that enables our small robot (length: 51 cm, width: 20 cm, height: 12.7 cm, leg length: 16 cm) to reliably climb a wide range of regular, full-size stairs with no operator input during stair climbing. Experimental data of energy efficiency in a form of specific resistance during stair climbing is given. The results presented in this paper are based on a new half circle leg design that implements a passive, effective leg length change.

A new torque control strategy for brushless motors with minimum torque ripple and minimum copper losses while maintaining the phase currents under magnetic (or current) saturation is presented. The optimal control, a nonlinear map from desired torque and position to the motor's phase currents, is the closed form solution to a quadratic programming problem. Experimental results demonstrate virtually ripple-free torque and improved tracking accuracy. In case of magnetic or current saturation, the maximum torque capability of the motor is considerably increased.

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 presents a new dynamic walking controllers for quadrupedal robots with compliant legs. The algorithm implements a "walking bound" gait, requires only one actuator per leg at the hip, and commands a constant hip velocity during stance. The algorithm has been implemented successfully on our Scout II quadruped robot and has yielded stable walking for ranges of operating conditions with minimal reliance on feedback. The experimental data is used to illustrate important considerations on torque generation that need to be taken into account both for successful implementations and realistic modeling of legged robots. In addition, we quantify the energetics of our walking experiments via the specific resistance and document dramatic differences between mechanical and electrical power.

A locking, unactuated knee is added to the Scout II quadruped robot and trotting gaits are studied. The mechanical design of the knee is presented, trotting algorithms are discussed, and a control approach for a robotic leg with an unactuated knee is developed. A model of a single leg is used to determine appropriate leg trajectory parameters and initial conditions to achieve trots. The single leg system and the complete robot are simulated. Experimental implementation of single leg control and quadruped trotting on Scout II are presented.

We have constructed an autonomous quadruped, Scout II, which features only a hip actuator and a passive compliant prismatic joint per leg. In this paper we demonstrate in simulation the control of stable running via two control strategies. One of them is verified experimentally on Scout II at a running speed near 1.2 m/s. The simulation model is verified experimentally.

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.

This paper reports on advances in the design and development of a high performance direct-drive joint for robotics and automation. The key design aspects of the mechanical components, sensors, control architecture, and a hydraulically actuated dynamometer testbed are described. We also present a number of advanced implementations in control, motor torque control, and motion control using positive joint torque feedback. Experimental results illustrate outstanding performance regarding thermal response, torque ripple, reference trajectory tracking, torque disturbance rejection, and joint stiffness.

This paper presents the experimental implementation of an energy efficient "controlled passive dynamic running" strategy on a planar one-legged running robot with hip and leg compliance. We (1997) introduced the approach previously via simulations, and tested via preliminary experiments. The improved version described here permits running speed of up to 4.5 km/h with a total mechanical power expenditure of only 48 W, which translates into a specific resistance of only 0.22. This is the highest efficiency among all actively controlled legged robots.

In our previous work (1998) we have shown that walking can be implemented on quadrupeds with stiff legs and only one actuated degree of freedom in the hip, based on the concept of controlled momentum transfer. In this paper we show via simulations and experiments on two different quadruped robots that dynamically stable and robust walking can be achieved via an open loop controller which is active only during the back leg support phase.

Positive joint torque feedback can compensate the detrimental effects of load torques on position tracking performance. However, with (real world) nonideal torque sources, simple unity gain positive torque feedback can actually deteriorate the performance, or even result in instability. An H/sup /spl infin// joint torque feedback is proposed which takes the dynamics and uncertainty of the actuator into account and minimizes the system's sensitivity to load torques. In our experimental direct-drive system, the H/sup /spl infin// positive torque feedback inner loop drastically improved the disturbance attenuation (25 dB) and load decoupling properties of a simple PID position controller.

A simple mechanical design for quadrupedal locomotion, termed SCOUT, is proposed, featuring only one degree of freedom per leg. The paper demonstrates experimentally that our first prototype SCOUT-1 is capable of walking, turning, and climbing over a step, despite its mechanical simplicity. The underlying principle is dynamic operation, based on controlled momentum transfer. Simulations show successful walking, stair climbing and running.

The open-loop torque control of synchronous motors with minimum torque ripple and minimum copper losses is presented. The control problem is viewed as an optimization problem for the nonlinear mapping from desired torque and position to the motor's phase currents. The performance of the controller to produce virtually ripple-free torque and to enhance the precision of position tracking is demonstrated experimentally.

This paper addresses the dynamics and control of direct drive robots with positive joint torque feedback. We analytically derive the system dynamics in closed form. Even though it is coupled and nonlinear in general, it is substantially simpler than the robot link dynamics. We also derive conditions on the robot configuration which result in linear dynamics. Motion control laws for both cases are proposed.

Applying positive joint torque feedback in direct drive motor systems reduces the effect of external load torques. This is most beneficial when accurate position tracking is required in the presence of large disturbances or for complex loads as found in robotic manipulators. We formulate the problem of torque feedback in the presence of actuator dynamics. The problem of finding the optimal torque feedback which minimizes the maximum disturbance sensitivity is equivalent to the model-matching problem. The effect of the load on the rotor dynamics appears as a perturbation minimized by the proposed torque feedback. To synthesize the torque filter, only the actuator dynamics and a very rough knowledge about the mechanical load is required.

We present a control strategy for a simplified model of a one-legged running robot which features compliant elements in series with hip and leg actuators. For this model, proper spring selection and initial conditions result in "passive dynamic" operation close to the desired motion, without any actuation. However, this motion is not stable. Our controller is based on online calculations of the desired passive dynamic motion which is then parametrized in terms of a normalized "locomotion time". We show in simulation that the proposed controller stabilizes a wide range of velocities and is robust to modeling errors. It also tracks changes in desired robot velocity and remains largely passive despite a fixed set of springs, masses, and inertias. Comparisons of simulated runs with direct hip actuation show 95% hip actuation energy savings at 3 m/s. Such energy savings are critical for the power autonomy of electrically actuated legged robots.

To study the design, control and energetics of autonomous dynamically stable legged machines we have built a planar one-legged robot, the ARL Monopod. Its top running speed of 4.3 km/h (1.2 m/s) makes it the fastest electrically actuated legged robot to date. We adapted Raibert's control laws for the low power electric actuation necessary for autonomous locomotion and performed a detailed energetic analysis of our experiments. A comparison shows that the ARL Monopod with its 125 W average power consumption is more energy efficient than previously built robots.

This paper presents a new model reference adaptive control method to control motor torque in direct drive reluctance motors in an accurate and ripple-free fashion. It is based on the motor's voltage equation and requires only measurements of motor angle, winding voltages and currents. In addition, we introduce a new optimal torque-to-current conversion which minimizes copper losses. Simulations of a reluctance motor with magnetically coupled phases demonstrate fast parameter convergence and accurate torque tracking.

We present a new approach for vertical motion feedback control of a hopping robot. The task of the feedback control is to stabilize the robotic system to a desired limit cycle under existing constraints on the controls. Unlike most previous methods, the approach presented here does not rely on the construction of the Poincare map, which simplifies the subsequent analysis, but can be difficult or impossible to obtain analytically. The method can also be applied to more complicated, possibly nonlinear models of legged robots, as well as other variable structure systems.

We present a control strategy for a simplified model of a one legged running robot which features compliant elements in series with hip and leg actuators. Proper spring selection and initial conditions result in "passive dynamic" operation close to the desired motion, without any actuation. However, this motion is not stable. The proposed controller is based on online calculations of the desired passive dynamic motion and stabilises any fixed robot speed. It also tracks large changes in desired robot velocity and remains largely passive for a wide range of velocities, despite a fixed set of springs, masses and inertias. To this end the desired motion is expressed as a function of a normalized "locomotion time" parameter. Comparisons of simulated runs with direct hip actuation show dramatic energy savings of 95% at 3m/s. Such energy savings are critical for the power autonomy of electrically actuated legged robots.

Introduces new compliance models for LADD (linear to angular displacement device) transmissions which reduce, by an order of magnitude, inelastic model errors of up to 18% full scale over force and position operating ranges. Elastic models introduced so far were all based on fiber elasticity, which show an increase an LADD length from the inelastic length with force. The authors show that in experiments the opposite is true. The LADD is always shorter than predicted from the inelastic model. As the load force increases, the LADD length approaches the inelastic length. The authors found the cause for this fundamentally different elastic behavior to be fiber bending. The authors also employ one of the new models to improve the prediction of the kinematics of a CLADD, which consists of two concentric LADD devices. The new LADD models are essential for the design of LADD based systems, the online estimation of LADD forces, and accurate control.

A recently developed kinematic calibration technique for six degree-of-freedom (DOF) arms, the Jacobian measurement method, is generalized to include underconstrained and overconstrained arms. Using joint torque sensing and a wrist six-axis force/torque sensor to measure the Jacobian, experimental results are presented for the first five DOFs of the Sarcos Dextrous Arm. Results are compared to two standard calibration methods, i.e., open loop calibration and circle point analysis. Measurements of endpoint position and orientation were obtained with the Optotruk and the Bird sensor, two commercial motion tracking systems.

The authors introduce a new control problem: the control of motion simulating devices (virtual motion systems (VMS)) for walking and running humans and robots in a fashion that feels most realistic, that is, like locomoting on ground. After developing simplified dynamical models for the VMS, the human/robot and the resulting coupled system, the authors cast the problem in terms of a performance index. This approach permits application of standard optimal control theory. They present two solutions and discuss upcoming problems in the task domain of virtual motion control.

The authors report progress towards model based, dynamically stable legged locomotion with energy efficient, electrically actuated robots. The present the mechanical design of a prismatic robot leg which is optimized for electrical actuation. A dynamical model of the robot and the actuator as well as the interaction with ground is derived and validated by demonstrating close correspondence between simulations and experiments. A new continuous, and exactly implementable open loop torque control algorithm is introduced which stabilizes a limit cycle of the underlying fourth order intermittent robot/actuator/environment dynamics.

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.>

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 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.>