There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Bilateral teleoperation: An historical survey

Biped robots form a subclass of legged or walking robots. The study of mechanical legged motion has been motivated by its potential use as a means of locomotion in rough terrain, as well as its potential benefits to prothesis development and testing. The paper concentrates on issues related to the automatic control of biped robots. More precisely, its primary goal is to contribute a means to prove asymptotically-stable walking in planar, underactuated biped robot models. Since normal walking can be viewed as a periodic solution of the robot model, the method of Poincare sections is the natural means to study asymptotic stability of a walking cycle. However, due to the complexity of the associated dynamic models, this approach has had limited success. The principal contribution of the present work is to show that the control strategy can be designed in a way that greatly simplifies the application of the method of Poincare to a class of biped models, and, in fact, to reduce the stability assessment problem to the calculation of a continuous map from a subinterval of R to itself. The mapping in question is directly computable from a simulation model. The stability analysis is based on a careful formulation of the robot model as a system with impulse effects and the extension of the method of Poincare sections to this class of models.

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Asymptotically stable walking for biped robots: analysis via systems with impulse effects

Bipedal locomotion is among the most difficult challenges in control engineering. Most books treat the subject from a quasi-static perspective, overlooking the hybrid nature of bipedal mechanics. Feedback Control of Dynamic Bipedal Robot Locomotion is the first book to present a comprehensive and mathematically sound treatment of feedback design for achieving stable, agile, and efficient locomotion in bipedal robots.In this unique and groundbreaking treatise, expert authors lead you systematically through every step of the process, including:Mathematical modeling of walking and running gaits in planar robotsAnalysis of periodic orbits in hybrid systemsDesign and analysis of feedback systems for achieving stable periodic motionsAlgorithms for synthesizing feedback controllersDetailed simulation examplesExperimental implementations on two bipedal test bedsThe elegance of the authors' approach is evident in the marriage of control theory and mechanics, uniting control-based presentation and mathematical custom with a mechanics-based approach to the problem and computational rendering. Concrete examples and numerous illustrations complement and clarify the mathematical discussion. A supporting Web site offers links to videos of several experiments along with MATLAB® code for several of the models. This one-of-a-kind book builds a solid understanding of the theoretical and practical aspects of truly dynamic locomotion in planar bipedal robots.

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Feedback Control of Dynamic Bipedal Robot Locomotion

Biped robots have better mobility than conventional wheeled robots, but they tend to tip over easily. To be able to walk stably in various environments, such as on rough terrain, up and down slopes, or in regions containing obstacles, it is necessary for the robot to adapt to the ground conditions with a foot motion, and maintain its stability with a torso motion. When the ground conditions and stability constraint are satisfied, it is desirable to select a walking pattern that requires small torque and velocity of the joint actuators. We first formulate the constraints of the foot motion parameters. By varying the values of the constraint parameters, we can produce different types of foot motion to adapt to ground conditions. We then propose a method for formulating the problem of the smooth hip motion with the largest stability margin using only two parameters, and derive the hip trajectory by iterative computation. Finally, the correlation between the actuator specifications and the walking patterns is described through simulation studies, and the effectiveness of the proposed methods is confirmed by simulation examples and experimental results.

/pdf/planning-walking-patterns-for-a-biped-robot-18hxylrb20.pdf

Planning walking patterns for a biped robot

This paper proposes a model called the gravity-compensated inverted pendulum mode (GCIPM) to generate a biped locomotion pattern that is similar to the one generated by the linear inverted pendulum mode, but accommodates the free leg dynamics based upon its predetermined trajectory. When the biped locomotion based upon the linear inverted pendulum mode is applied to real biped robots, the stability of the robot is disturbed due to the fact that the neglected dynamics of free legs is not actually negligible, moving the ZMP (zero moment point) away from the presumed fixed point. The GCIPM includes the effect of the dynamics of the free leg in a simple manner This paper also presents a control method for biped robots based upon the computed torque. Simulation results show that the biped robot is more stable with the walking pattern generated by the proposed method combined with the controller than with the one by the inverted pendulum mode.

/pdf/biped-robot-walking-using-gravity-compensated-inverted-542agu23na.pdf

Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control

This paper proposes a control method for biped robot locomotion based on impedance control and impedance modulation. Both legs are controlled by the impedance control, where the desired impedance at the hip and the swing foot are specified. The impedance parameters are changed depending on the gait phase of the biped robot. To reduce the magnitude of impact and to guarantee a stable footing at foot landings on the ground, the damping coefficient of the impedance of the landing foot is increased drastically and the reference trajectory of the landing foot is reset at its initial contact with the ground. A series of computer simulations of a 12-degree-of-freedom (DOF) biped robot with a 6-DOF environment model which consists of nonlinear and linear compliant spring-and-dampers, shows that the proposed control method works well and is superior to position-oriented control methods such as the computed-torque control method in impact regulation during foot landings and adaptation to some ground irregularity.

Impedance control for biped robot locomotion

Bilateral teleoperation systems connected to computer networks, such as Internet, have to deal with varying communication time delay. The entire system is easy to become unstable due to irregular time delay. In this paper, we design a sliding-mode controller for the slave and an impedance controller for the master. We propose a modified sliding-mode controller, in which the nonlinear gain can be set independently of the time delay variation. The proposed controller effectively compensates the effects of the varying time delay which deteriorates the performance of the regular sliding-mode controller. We illustrate the validity of the proposed controller using simulations with 1-DOF master/slave bilateral teleoperation system.

/pdf/sliding-mode-controller-for-bilateral-teleoperation-with-281y7epduv.pdf

Jong Hyeon Park

Papers

Biped robot walking using gravity-compensated inverted pendulum mode and computed torque control

Impedance control for biped robot locomotion

Sliding-mode controller for bilateral teleoperation with varying time delay

Stable bilateral teleoperation under a time delay using a robust impedance control

Fuzzy-logic zero-moment-point trajectory generation for reduced trunk motions of biped robots