Controlling Velocity in Bipedal Walking: A Dynamic Programming Approach

We are interested in adding actuation to passive dynamic walkers to enable them to control their velocity. We control velocity by using dynamic programming to design control laws for each desired velocity. We consider three cases: a simulated planar compass gait walker, a simulated 3D compass gait walker with roll dynamics, and a simulated planar compass gait walker with a torso. Each of the walkers have massless legs. The actions include foot placement, ankle torque, and desired torso orientation. We use Poincar´e sections to define the state of the model, and thus choose a new action once per footstep. The optimization criterion is based on the effort of swinging the limbs, applying torques, and maintaining the desired velocity. By generating control laws at different desired velocities and then selecting the appropriate control law we are able to control velocity in each of these walkers, and smoothly transition between different velocities. Our results also indicate how complex nonlinear control laws can be approximated by gain-scheduled linear control laws.