Dynamic Programming for Globally Optimal Trajectory Solution

A Matlab implementation for finding a globally optimal joint trajectory solution to a redundant 3R robot in XY space (orientation is free).

The first trajectory (circle) used a cost function to approximate the orientation phi of the end-effector to horizontal, besides minimizing the squared norm of velocities.

The second and third trajectories (square and sine) minimized only the sum of square and cubic norms of joint velocities.

Based on papers:

[1] E. Ferrentino, P. Chiacchio, “A topological approach to globally-optimal redundancy
resolution with dynamic programming”, ROMANSY 22 - Robot Design, Dynamics and Control, CISM International Centre for Mechanical Sciences, pp. 77-85, 2019.

and

[2] E. Ferrentino, P. Chiacchio, “On the Optimal Resolution of Inverse Kinematics for Redundant
Manipulators Using a Topological Analysis”, ASME Journal of Mechanisms and Robotics. June 2020; 12(3): 031002.