On Path Planning and Obstacle Avoidance for Nonholonomic Platforms with Manipulators: A Polynomial Approach

A planning methodology for nonholonomic mobile platforms with manipulators in the presence of obstacles is developed that employs smooth and continuous functions such as polynomials. The method yields admissible input trajectories that drive both the manipulator and the platform to a desired configuration and is based on mapping the nonholonomic constraint to a space where it can be satisfied trivially. In addition, the method allows for direct control over the platform orientation. Cartesian space obstacles are also mapped into this space in which they can be avoided by increasing the order of the polynomials employed in planning trajectories. The additional parameters required are computed systematically, while the computational burden increases linearly with the number of obstacles and the system elements taken into account. Illustrative examples demonstrate the planning methodology in obstacle-free and obstructed environments.