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The International Journal of Robotics Research, Vol. 24, No. 7, 523-536 (2005)
DOI: 10.1177/0278364905055377
© 2005 SAGE Publications

A Parametric Optimization Approach to Walking Pattern Synthesis

G. Bessonnet

Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France, bessonnet{at}lms.univ-poitiers.fr

P. Seguin

Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France

P. Sardain

Laboratoire de Mécanique des Solides, CNRS-UMR6610, Université de Poitiers, SP2MI, Bd. M. & P. Curie, BP 30179, 86962 Futuroscope Chasseneuil cedex, France

Walking pattern synthesis is carried out using a spline-based parametric optimization technique. Generalized coordinates are approximated by spline functions of class C3fitted at knots uniformly distributed along the motion time. This high-order differentiability eliminates jerky variations of actuating torques. Through connecting conditions, spline polynomial coefficients are determined as a linear function of the joint coordinates at knots. These values are then dealt with as optimization parameters. An optimal control problem is formulated on the basis of a performance criterion to be minimized, representing an integral quadratic amount of driving torques. Using the above spline approximations, this primary problem is recast into a constrained non-linear optimization problem of mathematical programming, which is solved using a computing code implementing an SQP algorithm. As numerical simulations, complete gait cycles are generated for a seven-link planar biped. The only kinematic data to be accounted for are the walking speeds. Optimization of both phases of gait is carried out globally; it includes the optimization of transition configurations of the biped between successive phases of the gait cycle.

Key Words: walking pattern synthesis • dynamics-based optimization • spline-based parametric optimization


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