Jerk-continuous Online Trajectory Generation for Robot Manipulator with Arbitrary Initial State and Kinematic Constraints

This work presents an online trajectory generation algorithm using a sinusoidal jerk profile. The generator takes initial acceleration, velocity and position as input, and plans a multi-segment trajectory to a goal position under jerk, acceleration, and velocity limits. By analyzing the critical constraints and conditions, the corresponding closed-form solution for the time factors and trajectory profiles are derived. The proposed algorithm was first derived in Mathematica and then converted into a C++ implementation. Finally, the algorithm was utilized and demonstrated in ROS & Gazebo using a UR3 robot. Both the Mathematica and C++ implementations can be accessed at https://github.com/Haoran-Zhao/Jerk-continuous-online-trajectory-generator-with-constraints.git