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Boundary Constraints


As we are solving a finite-time problem, the boundary constraints of the biped walking problem represent an important part of the problem definition. We allow a number of parameters to be variable. These are as follows:


At the initial and final time, periodicity of the states and controls must be enforced while in between phases continuity is enforced. Another boundary constraint is that if an impulsive liftoff force is included at the beginning of phase 1, then the velocities must reflect the sudden jump caused by the impulsive force. Given the magnitude of the impulsive force tex2html_wrap_inline746 , the Collision Algorithm can determine the resulting new velocities for the beginning of phase 1. A further boundary constraint is the swing leg must also land at the time of collision, tex2html_wrap_inline748 , at a step size equal to tex2html_wrap_inline750 . Since in our experiments we constrain the proportion of phase 1 to 85% of the total time of the walking step, the final or total time (also variable) may be determined from the phase 1 duration tex2html_wrap_inline748 .

Michael W. Hardt
Mon Oct 11 17:19:43 MET DST 1999