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.

/pdf/feedback-control-of-dynamic-bipedal-robot-locomotion-2pz7pbjgsi.pdf

Feedback Control of Dynamic Bipedal Robot Locomotion

Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set - a two-dimensional zero dynamics submanifold of the full hybrid model $whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.

/pdf/hybrid-zero-dynamics-of-planar-biped-walkers-1f08i7dzjl.pdf

Hybrid zero dynamics of planar biped walkers

We have been trying to induce a quadruped robot to walk with medium walking speed on irregular terrain based on biological concepts. We propose the necessary conditions for stable dynamic walking on irregular terrain in general, and we design the mechanical system and the neural system by comparing biological concepts with those necessary conditions described in physical terms. A PD controller at the joints can construct the virtual spring-damper system as the visco-elasticity model of a muscle. The neural system model consists of a central pattern generator (CPG) and reflexes. A CPG receives sensory input and changes the period of its own active phase. The desired angle and P-gain of each joint in the virtual spring-damper system is switched based on the phase signal of the CPG. CPGs, the motion of the virtual spring-damper system of each leg and the rolling motion of the body are mutually entrained through the rolling motion feedback to CPGs, and can generate adaptive walking. We report on our experimen...

Adaptive Dynamic Walking of a Quadruped Robot on Irregular Terrain Based on Biological Concepts

Tactile sensing in dexterous robot hands - Review

An experimental study of a biped robot is presented. A new scheme named the "linear inverted pendulum mode" is utilized for controlling a biped walking on rugged terrain. The authors developed a six-DOF biped robot, "Meltran II," which has lightweight legs and moves in a two-dimensional vertical plane. To investigate the effects not well discussed in the theory, the authors carried out two experiments, the support phase experiment and the support exchange experiment. The support phase experiment was carried out to check the actual dynamics of a biped walking under the proposed control. It was shown that the dynamics of the robot can be regarded as linear even though the mass of the legs, which was neglected in the theory, exists. The support exchange experiment was performed to check leg support exchange. The authors found that a smooth leg support exchange is achieved by making the foot contact with a certain vertical speed and holding two-leg support for a certain short period. Based on these results, a whole biped control system was implemented. In the authors' experiment the robot walked over a box of 3.5 cm height at a speed of 20 cm/s.

Experimental study of biped dynamic walking

In this paper, realtime control of dynamic biped locomotion using sensor information is investigated. The authors used an ultrasonic range sensor mounted on the robot to measure the distance from the robot to the ground surface. During the walking control, the sensor data is converted into a simple representation of the ground profile in realtime. The authors also developed a control architecture based on the linear inverted pendulum mode which they proposed previously for dynamic walking control. Combining the sensory system and the control system enabled the authors' biped robot, Meltran II, to walk over ground of unknown profile successfully.

Adaptive gait control of a biped robot based on realtime sensing of the ground profile

An experimental study of a biped robot is presented. A new scheme, named the "linear inverted pendulum mode" is utilized for controlling biped walking on rugged terrain. We developed a 6 d.o.f. biped robot "Meltran II" which has light weight legs and moves in a two dimensional vertical plane. To check the effects not well discussed in the theory, we carried out two experiments, the support phase experiment and the support exchange experiment. The support phase experiment was carried out to check the actual dynamics of biped walking when using the proposed control. It was shown that the dynamics of the robot can be regarded as linear even though the mass of the legs, which was neglected in the theory, exists, The support exchange experiment was performed to check leg support exchange. We found that a smooth leg support exchange is achieved by making the foot contact with a certain vertical speed and holding two leg support for a certain short period. Based on these results, a whole biped control system was implemented. In our experiment the robot walked over a box of 3.5 cm height at a speed of 20 cm/s.

Experimental study of biped dynamic walking in the linear inverted pendulum mode

Recognition of the current location is important for a mobile robot to follow the planned path. Landmarks, which are assumed in the environment around the robot, are used to support this recognition. A mobile robot basically estimates its current location by dead-reckoning using the information of internal sensors. Information obtained by landmark measurement is used to cancel the estimation error which will grow as the travelling distance increases.In this paper we propose a method to select the most suitable landmark among the measurable landmarks from a current position by evaluating the update of the estimation error distribution. We use the extended Kalman filter to update the distribution of estimation error. We show the update characteristics of two types of landmarks, such as line landmarks and point landmarks. For the evaluation of the update we use the width of the distribution ellipse perpendicular to the direction of the path. Through the navigation simulation the effectiveness of the proposed method is confirmed.

https://www.jstage.jst.go.jp/article/jrsj1983/11/4/11_4_533/_pdf

Planning of Landmark Measurement for the Navigation of a Mobile Robot

For the control of a dynamic mobile robot, the attitude in gravity space is an important state of the robot. Usually, the attitude is difficult to detect by simply using the signals from sensors. For example, an external sensor contacting the ground suffers disturbances from the roughness of the ground; the integration of a gyroscope signal has the problem of drift; an inclination sensor does not indicate the direction of gravity when acceleration exists. To solve these problems, we propose a control method in which the attitude of a mobile robot is estimated by an observer considering the robot dynamics and using only the information obtained by internal sensors. We applied this method to a wheeled inverted pendulum as an example of a dynamic mobile robot. The estimation of the attitude was made with good accuracy using the signals from the rate gyroscope and the motor encoder, and the control of stable running of the pendulum on a flat level plane worked successfully. We also realized the running contro...

Kazuo Tani

Papers

Experimental study of biped dynamic walking

Adaptive gait control of a biped robot based on realtime sensing of the ground profile

Experimental study of biped dynamic walking in the linear inverted pendulum mode

Planning of Landmark Measurement for the Navigation of a Mobile Robot

Estimation and Control of the Attitude of a Dynamic Mobile Robot Using Internal Sensors