Non-holonomic motion planning using dynamically consistent Jacobian inverse

Abstract

We propose a transfer of the concept of dynamically consistent Jacobian inverse from robotic manipulators to non-holonomic robotic systems. This transfer exploits an analogy between these two classes of systems established within the endogenous configuration space approach. Similarly as for robotic manipulators, the dynamic consistency of the Jacobian inverse for non-holonomic systems distinguishes itself by two features: it does not transmit some forces from the configuration space to the operational space, and it defines a decoupling of forces acting in the configuration space into a component coming from the operational space and an internal component affecting only the motion in the configuration space. The dynamically consistent Jacobian inverse is used to solve a motion planning problem for the rolling ball.