Research On Robot Motion Planning Based On Numerical Optimization

Numerical optimization-based motion planning methods have been widely used in recent years for various robotic platforms,and the ability to efficiently solve multi-objective multi-constraint problems has enabled robots to exhibit excellent motion performance.Such methods model the motion planning problem as a multi-objective multi-constraint optimization problem and use a series of numerical optimization methods to solve it.Numerical optimization methods refer to a series of algorithms that solve optimization problems in a numerical iterative way,and the direct solution belongs to a special numerical solution.The core and difficulty of such methods lies in writing mathematical forms of decision variables,constraints and cost functions for specific tasks.To master such methods and overcome this difficulty,this paper will model a multi-objective multi-constraint optimization problem for a soccer robot ball-interception task and a tracked robot terraincrossing task,and solve them using different numerical optimization methods.The main work of this paper is as follows.First,the relevant theoretical knowledge of such methods is summarized in order to establish the foundation for the designing of motion planning algorithms for different robotic platforms.The concepts and important properties of spline curves such as B-spline curves are summarized,and the general process of applying the concept of Signed Distance Field and its gradient and the concept of Direct Collocation Method to the modeling process of multi-objective multi-constraint optimization problems is given.Second,a motion planning algorithm based on motion primitives is proposed for the ball-interception behavior of the soccer robot,and a mathematical form of the multiobjective multi-constraint optimization problem is given for the ball-interception behavior,and implemented according to the idea of combining nonlinear constraints and cost functions with Quadratic Programs.The algorithm first models the kino-dynamic constraints and terminal constraints of each degree of freedom motion as a Quadratic Programming problem,derives the analytic solution of the Quadratic Programming problem based on the principle of Maximum Principle,then determines the candidate motion primitives in the analytic solution based on different ball-interception postures,and finally obtains the final trajectory from the nonlinear constraints and cost functions in the candidate primitives.Finally,simulation experiments and real experiments prove that the method is efficient,safe and real-time.Lastly,a motion planning algorithm based on posture prediction is proposed for the arbitrary-shaped terrain-crossing task of a tracked robot,which models the posture prediction problem in the terrain-crossing task as a multi-objective multi-constraint optimization problem and solves it based on a nonlinear programming solver.This paper first proposes a new B-spline curve-based tracked robot-terrain simplified contact model,which is used to transform the robot posture prediction problem into a position planning problem with control points,and then the problem is extended into a real-time motion planning problem by modifying the cost function of the static posture prediction problem,and finally,the control point shape relationship will be translated into the desired flipper angle and sent down to the actuator.Finally,simulation experiments and real experiments verify the effectiveness,real-time and continuity of the method.