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Given starting and ending positions and velocities, L2 bounds on the acceleration and velocity, and the restriction to no more than two constant control inputs, this paper provides routines to compute the minimal-time path. Closed form solutions are provided for reaching a position in minimum time with and without a velocity bound, and for stopping at the goal position. A numeric solver is used to reach a goal position and velocity with no more than two constant control inputs. If a cruising phase at the terminal velocity is needed, this requires solving a non-linear equation with a single parameter. Code is provided on GitHub 1 , extended paper version at [1]. [1] https://github.com/RoboticSwarmControl/MinTimeL2pathsConstraints/more » « less
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Zhao, Haoran; Abdurahiman, Nihal; Navkar, Nikhil; Leclerc, Julien; Becker, Aaron T. (, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS),)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.gitmore » « less
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