Imagine that you have designed a human-like biped robot and its first task is to move on a straight line. How would you control such a robot? With respect to this task of simple straight-line walk, the biped robot is a highly redundant system -- it has many more degrees of freedom (joints) than are kinematically necessary to perform walking. In order to specify the motions of the extra joints one may perhaps formulate an optimal control problem based on either minimum time, minimum joint travel, minimum power, or minimum energy. All these criteria are reasonable but what if the resulting motion does not appear human-like? Does human walk correspond to any optimal criterion at all?

It has been conjectured that human locomotion optimizes calorific energy per unit distance traveled although the energy surface is shallow around the minimum. Also conjectured, and perhaps more likely is the possibility that if human locomotion is indeed optimal, it is guided by a multi-criteria cost function. The available literature on the optimality of human locomotion is rich in theory and ingenious suggestions with very little decisive experimental validation. Also not well-understood are the effects of limb size, physical deformity on the optimal criteria.

Our work on a 4 dof planar biped robot model suggests that a robot with anthropomorphic proportions (geometric and inertial) may execute a natural swing phase almost passively. This confirms the results of other researchers, both in biomechanics and robotics. Our ongoing work seeks optimal control schemes for a complete gait cycle, one that includes the swing phase, the double support phase and the crucial short-duration transition phases.

A list of my papers on this topic:

**Generation of energy-optimal complete gait cycles for biped robots**- L. Roussel, C. Canudas de Wit, and
**A. Goswami** - IEEE Int. Conf. on Robotics and Automation, Leuven, Belgium, May 1998.

**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.

**Comparative study of methods for energy-optimal gait generation for biped robots**- C. Canudas de Wit, L. Roussel, and
**A. Goswami** - Int. Conf. on Informatics and Control, St. Petersburg, Russia, June 1997.

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