Smooth Planning for Manipulator with Multi-dimensional Actuator based on Quintic B-spline

Abstract

In order to solve the impact problem of uneven velocity during continuous operation for manipulator with multi-dimensional actuator, a smooth planning scheme based on Quintic B-spline algorithm was proposed. Firstly, the physical model of multi-dimensional actuator and its working principle were introduced. At the same time, the motion of the output axis vertex in space was decomposed into three steps, which can make the position relationship between the points more intuitive and convenient for our study. Secondly, the characteristics of Quintic B-spline algorithm were analysed. In this step, the B-spline interpolation function was defined at first, and the basis function of polynomial of degree p was defined according to the relevant information and its characteristics were indicated. Then, we analysed the node sequence parameters. For Quintic B-spline algorithm, when the position sequence of the rotor running track was given, three conditions must be satisfied to uniquely determine the corresponding B-spline function, namely: node vector, control vertex and the degree p of the B-spline curve. On this basis, the boundary constraints and control vertices were solved, which was a very important step. By solving the control vertices of Quintic B-spline curve, a smooth and continuous angular displacement curve can be obtained. The addition of four boundary conditions greatly increases the controllability of the system, making the rotor can start and stop in any way within the constraint conditions, and the connection of each interpolation point is smooth and continuous. The Quintic B-spline algorithm interpolation curve was obtained by simulation based on the time-position sequence of the actuator interpolation points. The results of the interpolation curve verified the effectiveness of the Quintic B-spline algorithm. In addition, three continuous running planning conditions were designed for the same interpolation sequence of the rotor to verify the controllability of the algorithm to the angular velocity and angular acceleration of the rotor during operation. The simulation results show that the Quintic B-spline algorithm has strong controllability for the angular velocity of actuator, and can effectively alleviate the soft impact of the system. Finally, a smooth planning experimental platform with multi-dimensional actuator was built. By setting the same trajectory and different interpolation points, the proposed Quintic B-spline algorithm was compared with the existing S-shaped curve planning algorithm based on the improvement. The results show that the proposed scheme has high control accuracy and strong impact mitigation performance, which can provide a reference for other multi-dimensional actuator trajectory planning.