TrajectTools

Polynomial trajectory generation tools for MATLAB. Analytical differentiation is calculated.

Features

• Arbitrary order trajectory
• Analytical differentiation
  No numerical differentiation, no delay
• Symbolic coefficients as well as numerical coefficients

Installation

addpath src to MATLAB

Requred toolbox

• Symbolic math toolbox
• Optional: FigTools

Case 1: Position constrained step trajectory

See example

Case 2: Position constrained back and forth trajectory

See example

Case 3: Velocity constrained back and forth trajectory

See example

Case 4: Acceleration constrained back and forth trajectory

See example

Case 5: Time-optimal 3rd order trajectory

Required additional toolbox

• Advanced Setpoints for Motion Systems
  Ref: M. Lambrechts, Paul; Boerlage, M.; Steinbuch, “Trajectory planning and feedforward design for electromechanical motion systems,” Control Eng. Pract., vol. 13, pp. 145–157, 2005.

See example

Case 6: Time-optimal 4th order trajectory

Required additional toolbox

• Advanced Setpoints for Motion Systems
  Ref: M. Lambrechts, Paul; Boerlage, M.; Steinbuch, “Trajectory planning and feedforward design for electromechanical motion systems,” Control Eng. Pract., vol. 13, pp. 145–157, 2005.

See example

Case 7: Jerk-optimal 5th order trajectory

Required additional toolbox

• splines.m
  Ref: W. Van Loock, G. Pipeleers, and J. Swevers, “B-spline parameterized optimal motion trajectories for robotic systems with guaranteed constraint satisfaction,” Mech. Sci., vol. 6, no. 2, pp. 163–171, 2015, doi: 10.5194/ms-6-163-2015.
• YALMIP
  Ref: J. Löfberg, “YALMIP : A Toolbox for Modeling and Optimiza- tion in MATLAB,” in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
• Appropriate solver
  e.g. MOSEK, SeDuMi

Jerk 2-norm minimization

See example

Case 8: Jerk-optimal 3rd order trajectory

Required additional toolbox

• splines.m
  Ref: W. Van Loock, G. Pipeleers, and J. Swevers, “B-spline parameterized optimal motion trajectories for robotic systems with guaranteed constraint satisfaction,” Mech. Sci., vol. 6, no. 2, pp. 163–171, 2015, doi: 10.5194/ms-6-163-2015.
• YALMIP
  Ref: J. Löfberg, “YALMIP : A Toolbox for Modeling and Optimiza- tion in MATLAB,” in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
• Appropriate solver
  e.g. MOSEK, SeDuMi

Jerk infinity-norm minimization

See example

Case 9: Jerk-optimal 5th order trajectory

Required additional toolbox

• splines.m
  Ref: W. Van Loock, G. Pipeleers, and J. Swevers, “B-spline parameterized optimal motion trajectories for robotic systems with guaranteed constraint satisfaction,” Mech. Sci., vol. 6, no. 2, pp. 163–171, 2015, doi: 10.5194/ms-6-163-2015.
• YALMIP
  Ref: J. Löfberg, “YALMIP : A Toolbox for Modeling and Optimiza- tion in MATLAB,” in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
• Appropriate solver
  e.g. MOSEK, SeDuMi

Weighted jerk 2-norm minimization

See example

Case 10: Time-optimal 5th order trajectory

Required additional toolbox

• splines.m
  Ref: W. Van Loock, G. Pipeleers, and J. Swevers, “B-spline parameterized optimal motion trajectories for robotic systems with guaranteed constraint satisfaction,” Mech. Sci., vol. 6, no. 2, pp. 163–171, 2015, doi: 10.5194/ms-6-163-2015.
• YALMIP
  Ref: J. Löfberg, “YALMIP : A Toolbox for Modeling and Optimiza- tion in MATLAB,” in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
• Appropriate solver
  e.g. MOSEK, SeDuMi

Time-optimal trajectory. More flexible than Case 6 but numerically sensitive

See example