Novel Manipulability for Parallel Mechanisms with Prismatic-Revolute Actuators, GA-DP Trajectory Planning Application

Abstract

Performance measures have been utilized for numerous applications in robotics research. In this paper, the manipulability and dexterity indices have been focused. These indices have been used successfully when parallel robots have either completely revolute or prismatic joints. But, in a manipulator with both revolute and prismatic joints, these may not be used because of the dimensional inconsistency of the components in the Jacobian matrix. Moreover, in the kinematic or dynamic case, for manipulability and dexterity analysis, the Euclidean norm for the velocity inputs is considered while the velocity inputs for active joints are generally independent; therefore, the manipulability and dexterity indices are explained based on the infinity-norm. Thus, the final solution is represented by the new concept of mixed manipulability polytope. Next, an example of the 3-RPC parallel robot is analyzed based on the notion of this index. As an application, the index is applied for trajectory planning in multi-objective optimal control. For this, one of the direct methods of optimal control, dynamic programming (DP), is selected. But for the DP, the genetic algorithm (GA) is used for searching the optimum path. This analysis is applied for a novel PU-3RPR redundant parallel manipulator. First, the parallel mechanism is introduced, and the kinematics and Jacobian analysis is discussed. Then the objective function that minimizes the pseudo kinetic energy and maximizes the index, is adopted for an optimization problem. Finally, the trajectory of the PU-3RPR redundant parallel mechanism is planned by the proposed GA-DP method.