Minimum-time trajectory planning for a 4-dof manipulator considering motion stability and obstacle avoidance

The trajectory planning with obstacle avoidance is a critical task for redundant manipulators in the complex operating environment. This paper proposes a time-minimum trajectory optimization technique to obtain a collision-free and jerk-continuous trajectory for a 4-dof redundant manipulator considering both kinematic and spatial constraints. In the optimization, the whole trajectory is divided into several sub-trajectories to ensure the reliability of the technique. The screw-based inverse kinematics (IK) model is used to obtain the angular displacements of joints corresponding to the end-effector final positions in each sub-trajectory. The spatial constraint is determined by assuming robotic links using cylinders with different bottom radius, and enveloping obstacles using spheres under different sizes. The quintic polynomial curve is utilized to interpolate in joint space to guarantee the continuous of the angular jerk of each joint. Finally, PSO algorithm is used to search for the optimal trajectory of the robot by taking the whole motion time as the optimization objective. Two cases are taken to validate the effectiveness of the proposed technique. The simulation results in MATLAB show that the robotic motion based on the optimal trajectory are safe, stable and efficient.