Smooth Jerk-Bounded Optimal Path Planning of Tricycle Wheeled Mobile Manipulators in the Presence of Environmental Obstacles

Abstract

In this work, a computational algorithm is developed for the smooth-jerk optimal path planning of tricycle wheeled mobile manipulators in an obstructed environment. Due to a centred orientable wheel, the tricycle mobile manipulator exhibits more steerability and manoeuvrability over traditional mobile manipulators, especially in the presence of environmental obstacles. This paper presents a general formulation based on the combination of the potential field method and optimal control theory in order to plan the smooth point-to-point path of the tricycle mobile manipulators. The nonholonomic constraints of the tricycle mobile base are taken into account in the dynamic formulation of the system and then the optimality conditions are derived considering jerk restrictions and obstacle avoidance. Furthermore, by means of the potential field method, a new formulation of a repulsive potential function is proposed for collision avoidance between any obstacle and each part of the mobile manipulator. In addition, to ensure the accurate placement of the end effector on the target point an attractive potential function is applied to the optimal control formulation. Next, a mixed analytical-numerical algorithm is proposed to generate the point-to-point optimal path. Finally, the proposed method is verified by a number of simulations on a two-link tricycle manipulator.