Lagrangian Jacobian Motion Planning: A Parametric Approach

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.

Modeling and control of a skid-steering mobile platform with coupled side wheels

This study is devoted to the modeling and control of a 4-wheel, skid-steering mobile platform with coupled side wheels, subject to lateral and longitudinal slips. The dynamics equations of the platform are derived, and 16 variants of motion distinguished. For the variant of motion allowing for all possible slips of the wheels two control problems are addressed: the motion planning problem and the trajectory tracking problem. The former problem is solved by means of a Jacobian motion planning algorithm based on the Endogenous Configuration Space Approach and, complementarily, using the Optimal Control Approach. The Nonlinear Model Predictive Control is applied to the latter problem. Performance of these control algorithms is illustrated by a sort of the parking problem. Significant robustness of the predictive control algorithm against the model uncertainty is revealed.