Optimal trajectory planning for robotic arms based on an improved adaptive multiobjective particle swarm algorithm
[Objective]Trajectory planning is critical for the motion control of a manipulator.The motion time and joint vibration of the manipulator can be reduced by providing a fast and stable reference trajectory to the controller.The single objective trajectory optimization algorithm remains insufficient in meeting the increasing production needs;therefore,it is often necessary to use a multiobjective heuristic algorithm to optimize the motion trajectory of the manipulator while satisfying its kinematic constraints to optimize the motion time and reduce the joint impact or energy loss,improving the production efficiency of the manipulator and ensuring its stability during motion.An improved adaptive multiobjective particle swarm optimization(IAMOPSO)method is studied for the time-and impact-based optimal trajectory planning of a multidegree-of-freedom manipulator.[Methods]First,to obtain physically continuous motion trajectories,including position,velocity,and acceleration,we use a quintic B-spline curve to interpolate the joint path points based on the local controllability of the curve.The trajectory optimization process is a step-by-step approach so that the interpolated solution optimally satisfies the kinematic constraints of the manipulator,and the B-spline curve passes through all interpolation points,rendering the motion trajectory of the manipulator more adaptable.Second,a specific objective function improves the motion efficiency of the manipulator.Under certain kinematic constraints,an expression for the joint impact of the manipulator is designed to improve the trajectory tracking accuracy and ensure the stability of the manipulator during operation tasks.Finally,to increase the diversity of the nondominated solution set while avoiding the local extremum,the multi-objective particle swarm optimization(MOPSO)algorithm is improved through a hybrid strategy of mutation operators,adaptive weights,and dynamic learning factors;consequently,the objective function is optimally solved,and the average optimal solution is selected using a normalization function.A nonlinear mutation operator is adopted to encourage particles to comprehensively explore the decision space,ensuring population diversity in the initial iteration of the algorithm,and an adaptive weight strategy and dynamic learning factor are adopted to balance the exploration and development of the MOPSO algorithm,making it easy for the algorithm to determine the global optimal solution.[Results]① The quintic B-spline curve accurately interpolates the path points and ensures the continuity of the acceleration and jerk curves,thus meeting the requirements of smoothness and continuity of the joint trajectory of the manipulator;② the optimal trajectory planning method based on the IAMOPSO algorithm can yield a Pareto front with good convergence,select the time-and impact-based optimal trajectory according to the average optimal criterion,and achieve continuity of joint angles and their derivatives.[Conclusions]The optimal trajectory planning method for the manipulator based on IAMOPSO proposed in this paper can improve the motion efficiency and tracking accuracy of the manipulator,obtain Pareto front surfaces with good convergence,ensure smooth and continuous joint curves of the manipulator,and improve the operational efficiency and stability of the manipulator.
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