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The motion planning problem for nonholonomic robotic systems is studied using the continuation method and the optimization paradigms. A new Jacobian motion planning algorithm is derived, based on a solution of the Lagrange-type optimization problem addressed in the linear approximation of the system. Performance of the new algorithm is illustrated by numeric computations performed for the unicycle robot kinematics.

This paper is devoted to the motion planning problem of nonholonomic robotic systems whose kinematics are represented by a driftless control system with outputs. The motion planning problem is defined in terms of the inversion of the end-point map of the system, that may be accomplished by a Jacobian algorithm. The Lagrangian Jacobian inverse is introduced and examined, and a corresponding Lagrangian Jacobian motion planning algorithm is designed. Performance of this algorithm is illustrated by solving a motion planning problem for the rolling ball.

This paper addresses the motion planning problem of nonholonomic robotic systems. The system's kinematics are described by a driftless control system with output. It is assumed that the control functions are represented in a parametric form, as truncated orthogonal series. A new motion planning algorithm is proposed based on the solution of a Lagrange-type optimisation problem stated in the linear approximation of the parametrised system. Performance of the algorithm is illustrated by numeric computations for a motion planning problem of the rolling ball.

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