Generation and Local Stabilization of Fixed Point Based on a Stability Mechanism of Passive Walking

Abstract-A passive walker with knees can walk down gentle slope in a natural gait and can exhibit a stable limit cycle. Though the passive walker is simple, it is a sort of hybrid system which combines the continuous dynamics of leg-swing motion and the discrete event of leg-exchange. We focus on the mechanisms of generation and stabilization of a fixed point of passive walking. We propose a generation method of fixed point based on its physical structure. We derive the local stabilization control method from a stability mechanism of a fixed point of passive walking. I. I Passive walking [1] can be regarded as a physical phenomenon generated by the hybrid system, which consists of continuous dynamics of leg-swing motion and discrete event of leg exchange. Gait generation and its stability must be analyzed from the hybrid system. Passive walking can exhibit a stable limit cycle. When the state keeps on the stable limit cycle, walking system is stable. McGeer Many dynamical systems reach an equilibrium state which condition is minimum or local minimum point of energy function. On the other hand, the fixed point of passive walking is known that it keeps a balance between the energy supplied by potential energy and the energy lost by heelstrike In recent years, several researchers [7]-[12] have studied walking robots based on passive walking. The robots can walk on level ground with efficient. These studies assume that a stable fixed point of passive walking exists. In some cases, fixed point of passive walking is not always generated, and is not always stable. The studies except for Passive walking has not only a stable fixed point but also a unstable fixed point. When 1-periodic gait turns 2-periodic Y. Ikemata, A. Sano and H. Fujimoto are with Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi, JAPAN [email protected] have proposed the stabilization control method based on the existing control method. These stabilization control methods are not particularly effective stabilization method of passive walking because these don't consider the stability mechanism of a fixed point of passive walking. In this paper, we focus on the mechanisms of generation and stabilization of a fixed point in passive walking. At first, we demonstrate the physical structure of a fixed point, and propose a generation method of a fixed point based on its physical structure. Secondly, we derive the local stabilization control method from a stability mechanism of a fixed point. Though our stabilization control method is very simple, the highest local stability of a fixed point can be achieved. Finally, the validity of our proposed methods of generation and stabilization is confirmed by the simulation. II. M A. Leg-swing motio

Locomotion and balance control of humanoid robots with dynamic and kinematic constraints

Building a robot capable of servicing and assisting people is one of the ultimate goals in humanoid robotics. To realize this goal, a humanoid robot first needs to be able to perform some fundamental locomotion tasks, such as balancing and walking. However, simply performing such basic tasks in static, open environments is insufficient for a robot to be useful. A humanoid robot should also possess the ability to make use of the object in the environment to generate dynamic motions and improve its mobility. Also, since humanoid robots are expected to work and live closely with humans, having human-like motions is important for them to be human-friendly. This dissertation addresses my work on endowing humanoid robots with the ability to handle dynamic and kinematic constraints while performing the basic tasks in order to achieve more complex locomotion tasks. First, as a representative case of handling dynamic constraints, a biped humanoid robot is required to balance and walk on a cylinder that rolls freely on the ground. This task is difficult even for humans. I introduce a control method for a humanoid robot to execute this challenging task. In order for the robot to be able to actively control cylinder's motion, the dynamics of the cylinder has been taken into account together with the dynamics of the robot in deriving the control method. Its effectiveness has been verified by full-body dynamics simulation and hardware experiments on the Sarcos humanoid robot. Second, as an example of tasks with kinematic constraints, I present a method for real-time control of humanoid robots to track human motions while maintaining balance. It consists of a standard proportional-derivative tracking controller that computes the desired acceleration to track the given reference motion and an optimizer that computes the optimal joint torques and contact forces to realize the desired acceleration, considering the full-body dynamics of the robot and strict constraints on contact forces. By taking advantage of the property that the joint torques do not contribute to the six degrees of freedom of the floating base, I decouple the computation of joint torques and contact forces such that the optimization problem with strict contact force constraints can be solved in real time. In full-body simulation, a humanoid robot is able to imitate various human motions by using this method. Through this work, I demonstrate that considering dynamic and kinematic constraints in the environment in the design of controllers enables humanoid robots to achieve more complex locomotion tasks, such as manipulating a dynamic object or tracking given reference motions, while maintaining balance.Doctor of Philosoph