Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point (ZMP). The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy, previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree-of-freedom subsystem of the closed-loop model. Since the ZMP is controlled, bipedal walking that includes a prescribed rotation of the foot about the toe can also be considered. Simple analytical conditions are deduced that guarantee the existence of a periodic motion and the convergence toward this motion.

Consider a biped evolving in the sagittal plane. The unexpected rotation of the supporting foot can be avoided by controlling the zero moment point or ZMP. The objective of this study is to propose and analyze a control strategy for simultaneously regulating the position of the ZMP and the joints of the robot. If the tracking requirements were posed in the time domain, the problem would be underactuated in the sense that the number of inputs would be less than the number of outputs. To get around this issue, the proposed controller is based on a path-following control strategy previously developed for dealing with the underactuation present in planar robots without actuated ankles. In particular, the control law is defined in such a way that only the kinematic evolution of the robot's state is regulated, but not its temporal evolution. The asymptotic temporal evolution of the robot is completely defined through a one degree of freedom subsystem of the closed-loop model. Simple analytical conditions, which guarantee the existence of a periodic motion and the convergence towards this motion, are deduced.

This study proposes the analysis of two control strategies for a planar biped. One control makes it possible to find and study the existence of a cyclic motion and its stability, in this approach the avoidance of unexpected rotation of the supporting foot is treated via the control of the center of pressure or CoP. When the task is a simultaneous control of the joints and of the CoP, the system becomes under-actuated in the sense that we have fewer inputs than outputs. This control law is designed to track a desired geometric evolution of the biped configuration, and not the temporal evolution. But the temporal evolution is completely defined and can be analyzed through the study of a model with one degree of freedom. The influence of the desired geometric evolution of CoP on the stability properties of the control law is studied. The second control law improve the performances of the first one by increasing the rate of convergence towards the cyclic motion and enlarging the basin of attraction of the control. This improvement of the performances is possible by forcing the convergence by the control and relaxing the CoP evolution to be within the foot limits

The objective of this study is to obtain optimal cyclic gaits for a biped without actuated ankle. For the walking, the gait is composed of successive single support phases and instantaneous double support phases that are modeled by passive impact equations. The legs swap their roles from one single support phase to the next one. During each phase the evolution of the joints variables is assumed to be polynomial functions of a scalar path parameter. The coefficients of the polynomial functions are chosen to optimise a torque criterion and to insure a cyclic motion for the biped. Furthermore, the optimal gait is defined with respect to given performances of actuators. The torques and velocities at the output of the gearbox are bounded. For this study, the physical parameters of a prototype are used. Initial starting motions that are composed of a double support and a transitional single support are also defined.

The objective of this study is to analyze the stability of control strategy for a planar biped robot. The avoidance of unexpected rotation of the supporting foot is treated via the control of the zero moment point or ZMP. When the task is a simultaneous control of the joints and of the ZMP, the system becomes under-actuated in the sense that there is less inputs than the number of outputs. The control law is defined in such a way that only the geometric evolution of the biped configuration is controlled, but not the temporal evolution. The temporal evolution during the geometric tracking is completely defined and can be analyzed through the study of a model with one degree of freedom. Simple conditions, which guarantee the existence of a cyclic motion and the convergence towards this motion, are deduced.