Nonlinear predictive control of unicycle robot (3): code , part II, core optimization

Antonio Sala, UPV

Difficulty: **** ,       Relevance: ,      Duration: 41:58

Summary:

This video continues with the detailed Casadi (+Ipopt) Python code analysis (basically line-by-line equivalent to the Matlab script also provided).

In the previous video [mpcunic2EN], the preliminary ideas were discussed (velocity constraints, number of waypoints, size of decision variables, unicycle robot state equation, initial guess based on linear interpolation of some heuristic waypoints, plus invented infeasible control actions).

In this video, we discuss the:

• Cost index, the integral of a loss function L(x,u)

• Integrator object, computing via Runge-Kutta 4 the next state and the accumulated cost from waypoint to waypoint

• The main loop defining $x_k$, $u_k$, $x_{k+1}$ and connecting them via the Integrator; also, constraints for $x_k$ being in a suitable rectangle being part of the safe corridor in the form $Ax\le b$.

• How the overall problem is cast, and then the optimizer is called.

For brevity, plotting/animation code is not explained, as it is out of the scope of the present video.

Actual runs of the code, with simulation and animations of the resulting trajectories will be the goal of video [mpcunic4EN], which will close the case study.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.