Polynomial-based obstacle avoidance techniques for nonholonomic mobile manipulator systems

A planning methodology for nonholonomic mobile manipulators in the presence of obstacles is developed. The method employs smooth and continuous functions, such as polynomials, and it is very fast, easy to use and computationally inexpensive. The core of the method is based on mapping the nonholonomic constraint to a space where it can be satisfied trivially. In this paper, the method is first extended to include polygonal obstacles of any kind, allowing for less conservative workspace representations. The algebraic nature of the methodology and its advantages are retained. To improve the performance of the method in finding collision-free paths with smaller length, two techniques are studied in detail. The first uses intermediate path points and the second exploits the periodicity of the trigonometric functions involved. The proposed methodology is also extended to the case of obstacles that are moving in the workspace with a priori known trajectories. This case is illustrated by an example of great application interest, in which the end-point follows a desired Cartesian trajectory while the platform and the manipulator follow valid and collision-free paths connecting given initial and final points. Additional illustrative examples demonstrate the planning methodologies in a variety of obstructed spaces.