A parametric optimization approach to walking pattern synthesis

Walking pattern synthesis is carried out using a spline-based parametric optimization technique. Generalized coordinates are approximated by spline functions of class C-3 fitted 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.