Examples of efficient trajectory optimization for robot motion planning

• chebfun - Numericaltool for Chebyshev function
• CasADi - Symbolic tool for automatic differentiation

Run MainDemo.m and follow instructions.

• [0] 2D scara robot, time optimal motion with kinematics constraints

• [1] 2D scara robot, obstacle avoidance with kinematics constraints

• [2] 2D scara robot, obstacle avoidance with dynamics constraints

• [3] 2D wafer handling robot, obscatle avoidance with kinematics constraints, description refer to "Trajectory planning for robot manipulators considering kinematic constraints using probabilistic roadmap approach." Xiaowen Yu etc., 2017, or "Intelligent Control and Planning for Industrial Robots." Yu Zhao, 2018.

• In regards of 6-axis robot cases, using FANUC M20iA model from ARTE. Implementation includes visualization, forward and inverse kinematics, inverse dynamics (recursive Newton Euler method, or rNE), and forward dynamics (articulated body algorithm, or ABA) for planning calculation. Some parameters have been modified from ARTE (zero offset, joint limit)

• [4] 6-axis robot, time optimal control under dynamic constraints (velocity bound, torque bound, and torque rate bound). Can choose whether using regularization term in cost function or not. If not, running 'pure' time optimal control result, which runs slower and returns motion a little bit wired to human.

• [5] 6-axis robot, time optimal control under dynamic constraints as [4] and obstacle avoidance constraints. Can choose whether using regularization term in cost function or not. Can choose whether to visualize boudning balls of robot links.

• [6] 6-axis robot, time optimal control under kinematic constraints (position, velocity, acceleration, jerk) and obstacle avoidance constraints. Can choose whether to visualize bounding balls of robot links.

Besides, a quadrotor demo can be found in another git repo

These examples demonstrate the work shown in "Efficient trajectory optimization for robot motion planning." (2018).

2D scara robot planning

3D 6-axis robot planning

• Zhao, Yu, Hsien-Chung Lin, and Masayoshi Tomizuka. "Efficient trajectory optimization for robot motion planning." 2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV). IEEE, 2018.
• Zhao, Yu. Intelligent Control and Planning for Industrial Robots. Diss. UC Berkeley, 2018.
• Yu, Xiaowen, et al. "Trajectory planning for robot manipulators considering kinematic constraints using probabilistic roadmap approach." Journal of Dynamic Systems, Measurement, and Control 139.2 (2017).

Please use

@inproceedings{zhao2018efficient,
  title={Efficient trajectory optimization for robot motion planning},
  author={Zhao, Yu and Lin, Hsien-Chung and Tomizuka, Masayoshi},
  booktitle={2018 15th International Conference on Control, Automation, Robotics and Vision (ICARCV)},
  pages={260--265},
  year={2018},
  organization={IEEE}
}

or

@phdthesis{zhao2018intelligent,
  title={Intelligent Control and Planning for Industrial Robots},
  author={Zhao, Yu},
  year={2018},
  school={UC Berkeley}
}