Time-optimal Trajectory Planning Based On Genetic Algorithm For Manipulator

This paper aims to plan a course of time optimal collision-free trajectories, and these trajectories are angular displacement, angular velocity, angular acceleration without mutations of each rod. We selected manipulator PUMA560as the research object, established kinematic model and dynamics model. We used B-spline to plan out some trajectory of the end of the robot arm. Using genetic algorithm, optimal time for the guidelines have been obtained to optimize the trajectory. Ultimately, we get the optimal time trajectory of the end of the robot arm. The main contents are as follows:First, we simplify geometry of the overall manipulator, establish the coordinate of a link, use the D-H method to establish the transformation matrix, obtain manipulator kinematics equations which are based on the model parameters and the theoretical basis of the kinematic, calculate forward kinematics equations of the PUMA560, do the simulation with ADAMS. The results of simulation is similar with calculations to verify the correctness of the manipulator forward kinematics equations. Then, we do inverse kinematics analysis in order to lay the groundwork for the subsequent trajectory planning.Secondly, considering the strong coupling and nonlinear dynamic equations, we made some simplification of the kinetic equations before solving the kinetic equation of each joint of manipulator. We simplify the speed, kinetic and potential energy. We select Lagrange equation method to establish the kinetic equation of each joint of the robot arm based on the geometric parameters and the inertia parameters of the rod. We calculate the transformation matrix of each joint, the pseudo inertia matrix of each joint and the system inertia matrix of each joint.Thirdly, we introduce some trajectory planning method from two space. The two space are joint space and Cartesian space. For the joint space trajectory planning, we introduce cubic polynomial trajectory planning and five polynomial trajectory planning without intermediate interpolation points; we introduce4-3-4trajectory planning method with intermediate points and3-5-3trajectory planning methods with intermediate points, as well as cubic spline interpolation and cubic B-spline curve trajectory planning. For cartesian space trajectory planning, we introduce linear interpolation and circular interpolation trajectory planning. In this paper, we adopt the B-spline to accomplish trajectory planning. We draw some intermediate interpolation points (data points) on a given trajectory interpolation. These obtained data points are transformed into joint angle values with inverse kinematics. The restrains that are in Cartesian trajectory space are transformed into the joint space. Then, we use B-spline to fit each joint trajectory. While, the data was introduced into ADAMS to simulate the trajectory planning. We gain angle displacement curve, angular velocity curve and angular acceleration curve of each joint. Form the curve, we can see that the speed changes gently, but the angular acceleration curve has distinct mutations. And the entire running time of the track is11s, the time is not the best. So the trajectory also cannot come to be optimized.Finally, setting the optimization objective is the time, we selecte the genetic algorithms to optimize the entire manipulator trajectory. We briefly introduce the principles of genetic algorithm. Considering the angular velocity constraint, the angular acceleration constraint, angular acceleration constraints and torque variation constraints, we use genetic algorithms to optimize the obtained B-spline trajectory. We set time as the optimization objectives. We give the specific optimization steps. Ultimately, we got B-spline time optimal trajectory meeting the kinematic constraints and dynamic constraints.