Nonholonomic Motion Planning Strategy for Underactuated Manipulator

Abstract

This paper develops nonholonomic motion planning strategy for three-joint underactuated manipulator, which uses only two actuators and can be converted into chained form. Since the manipulator was designed focusing on the control simplicity, there are several issues for motion planning, mainly including transformation singularity, path estimation, and trajectory robustness in the presence of initial errors, which need to be considered. Although many existing motion planning control laws for chained form system can be directly applied to the manipulator and steer it to desired configuration, coordinate transformation singularities often happen. We propose two mathematical techniques to avoid the transformation singularities. Then, two evaluation indicators are defined and used to estimate control precision and linear approximation capability. In the end, the initial error sensitivity matrix is introduced to describe the interference sensitivity, which is called robustness. The simulation and experimental results show that an efficient and robust resultant path of three-joint underactuated manipulator can be successfully obtained by use of the motion planning strategy we presented.

Path Planning for Chainable Non-holonomic System Based on Iterative Learning Control

“…The position error of the chain variable changed with the number of iterations, in that the target configuration error function e(c [k] ) of the system converged exponentially to the target configuration. According to the evaluation index of linear approximation of non-holonomic systems [18], the iterative trajectory of the system is not satisfactory at φ2=36.6°, and the planned path of joint 1 deviated from the linear reference path (the segment between the initial and target configurations) by 59.63° at the most. There were 2 extreme values on the trajectory relative to the reference path, indicating that joint 1 turned twice during the movement.…”

“…To solve the problem, it is necessary to identify the nonlinear mapping between the chain space and configuration space, and select the input parameters based on the error tolerance coefficient, thus reducing the sensitivity of the manipulator system to the initial error and enhancing the open-loop robustness and operability of path planning. The specific steps are detailed in Reference [18].…”

Nonholonomic Motion Planning Using Trigonometric Switch Inputs

“…Measurement and control system for underactuated manipulator is described in [11]. The polynomial input control for an under actuated manipulator was studied in [12]. Chelouah et al demonstrated the effectiveness of the digital control method through two classic examples: the car with one trailer and the hopping robot [13].…”