Motion planning in endogenous configuration space

We consider a motion planning problem for the mobile manipulator composed of a nonholonomic mobile platform and a holonomic manipulator fixed to the platform. The problem consists of driving the end effector to a desirable location in the task space, and avoiding simultaneously a collision of the end effector with obstacles present in the task space. Our main objective is to demonstrate that a natural strategy of solving this problem, based on adding a specific self-motion component to the motion produced by the Jacobian inverse kinematics algorithm, is applicable within the endogenous configuration space approach. The instantaneous kinematics and analytic Jacobian of the mobile manipulator are defined in the endogenous configuration space. A general Jacobian pseudo-inverse algorithm is used as a basic tool for solving the inverse kinematic problem. On an assumption that in the task space of the mobile manipulator there exists a collection of obstacle events specifying forbidden end effector positions and orientations in given time instants, we design a motion planning algorithm whose principal idea relies on generating a direction of motion in the endogenous configuration space, that repels the endogenous configuration from the closest obstacle event. The performance of the motion planning algorithm is illustrated by computer simulations.