Quasi-static motion planning on uneven terrain for a wheeled mobile robot

In this paper we present a motion planning algorithm connecting a starting and ending goal positions of a wheeled mobile robot (WMR) with a passive variable camber (PVC) on a fully 3D uneven terrain without slipping. The overall planning framework is along the lines of the RRT (Rapidly Exploring Random Tree). The curve connecting the adjacent nodes of the RRT is a quasi-static path which is generated using the forward motion problem based on the Peshkin´s minimum energy principle which combines the force and kinematic relationships of the WMR into a nonlinear optimization problem. The output of this optimization routine is a set of ordinary differential equations (ODEs) representing the non-holonomic constraints and wheel ground contact conditions of the robot along with a set of differential algebraic equations (DAEs) representing the geometric/holonomic constraints of the robot. In general a complete simulation of a WMR on a fully 3D terrain has been a difficult problem to solve. Previous methods for continuous evolution of the WMR have only incorporated the wheel ground contact constraints within the DAE framework. This work goes beyond the previous methods by incorporating the quasi-static and friction cone constraints within the DAE framework. This evolution is now extended to a motion planning algorithm which guarantees that the vehicle traverses along quasi-static stable paths.