Collision-free path planning of a novel reconfigurable mobile parallel mechanism

Abstract

This paper initially deals with the design of a new customized reconfigurable mobile parallel mechanism. This mechanism is called the ‘Taar Reconfigurable ParaMobile’ (TRPM), consisting of three mobile robots as the main actuators. Then, the kinematics and path planning for this mechanism are presented. The newly proposed mechanism is expected to circumvent some shortcomings of inspection operation in unknown environments with unexpected changes in their workspace, for example, in a water pipe with a non-uniform cross-sectional area. In this paper, ‘Artificial Potential Field’ (APF) has been assumed to be the path planning algorithm and its resulting attractive and repulsive forces are only applied to the end-effector to generate the desired path. It is worth mentioning that the obstacle considered in this paper is a wedge which models an environment with non-uniform cross-sectional area along the path travelled by the end-effector. The inverse kinematics of the TRPM is then solved by resorting to the Resultant method as well as the Homotopy continuation method. The objective of utilizing these two well-known methods is to verify the correctness of the upper bound of solutions. It should be mentioned that solving the inverse kinematic problem obtained from both above-mentioned methods, leads to 12 solutions: eight real and four complex solutions. As a novel parallel mechanism, the TRPM yields a three-degrees-of-freedom kinematic redundancy. Despite the fact that the redundancy is sometimes beneficial for the control procedure, solving the inverse kinematics of the TRPM would be feasible only by adding some constraints. As a result, there will be a system of equations consisting of three kinematic equations and three auxiliary equations. Results from this study reveal that, by applying APF as the path planning algorithm to the TRPM, it is possible to track proper paths to reach the target.