Motion planning algorithm for a bipedal walker

Mathematically, bipedal walking can be modeled as a combination of two serial manipulators, namely stance leg and swing leg, having two revolute type joints (two R–R type serial manipulators). During motion, each leg changes its state from stance leg to swing leg periodically and it is assumed that the legs can only be in the same phase (stance leg phase) at the beginning and at the end of the motion. In walking phenomenon, trajectories of hip and knee articulations have great importance for the reason that they guarantee the synchronized movement of the joints thereby yielding a stable walking characteristic. The proposed trajectory planning procedure and detailed analyses are summarized as follows: • First, the space curve, which passes through all of the desired points along hip trajectories is specified. • Then, parameters of hip trajectory curve are specified to assure that the hip tracks this curve with the desired velocity and acceleration values. • Using inverse dynamics and coupling transformations, joint variables are calculated in time domain. • For ankle trajectory, three critical points corresponding to extremum poses of bipedal walker is defined. These are the start point, mid-point and point of one step motion. • By solving kinematic equations of the bipedal walker, the joint angles of swing and stance legs are obtained for the given poses. • Time-dependent angular position parameters are calculated in configuration space. In this study a parametric algorithm for motion planning procedure of a bipedal walker by following the above steps are presented and the reachability of the resultant trajectories is verified using forward and inverse kinematical models of the reference bipedal walker.