Continuation method approach to trajectory planning in robotic systems

This paper uses the continuation method as a guideline to address the trajectory planning problem in robotic systems. It is assumed that the robotic system can be represented by a control affine system with output. From the homotopy map a partial differential equation is derived involving the control system and its variational system, whose solution yields a 1-parameter family of control functions. This family contains a solution to the trajectory planning problem, corresponding to the parameter growing up to infinity. The approach developed in the paper is illustrated with a trajectory planning problem for the kinematics of the rolling ball.