Impactive dynamic systems

Understanding human walking as well as machines with backlash

This work is done with Marco Mata and Bernard Brogliato from LAG-ENSIEG, Grenoble, France.

It is known that impacts can profoundly alter the behavior of dynamic systems. Impacts may occur in a broad class of systems. At every heel touchdown during human walking, the swinging leg comes to a complete stop which gives rise to a large foot/ground force. This can be considered as an impact and has a fundamental importance on the human gait. It is thought that the evolution of the human leg structure and the associated kinematics and dynamics has been driven, among other objectives, to minimize the detrimental effects of impact on the human body. Our initial efforts involve the modeling and control of interaction between simple non-linear compliant systems with and without friction.

Impacts involving much larger force spikes and much sharper velocity discontinuities may take place in mechanical systems. The clearance between two moving machine parts, due such effects as gear backlash, machining imprecision (however small) and thermal effects, favors the occurrence of impacts in these systems. Impacts are known to be responsible for chattering and instability problems in machines and is extremely difficult to control.

We use the so-called impact damper model in order to study the phenomenon of dynamic backlash including its inherent non-linearities. We propose a PD control scheme to generate periodic trajectories in this system. We show that appropriate gains in the PD control scheme can be selected such that the closed-loop system is locally stable around a desired symmetric periodic orbit. We use the impact Poincare map to demonstrate the local stability of the motion induced by the controller. In order to enlarge the basin of attraction of this orbit we propose the use of a hybrid control in addition to the PD control.

A list of my papers on this topic:

On the control of mechanical systems with dynamic backlash
M. Mata-Jimenez, B. Brogliato, and A. Goswami
CDC Conf, San Diego, CA, December 1997.
Analysis of PD control of mechanical systems with dynamic backlash
M. Mata-Jimenez, B. Brogliato, and A. Goswami
2nd Int. Symp. MV2 on Active Control in Mechanical Engineering, Lyon, France, October 1997.
Periodic stabilization of a 1-dof hopping robot over nonlinear compliant surface
C. Canudas de Wit, L. Roussel, and A. Goswami
IFAC Symp. on Robot Control (SyRoCo), Nantes, France, September 1997.
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