Nonlinear predictive control of unicycle robot (1): problem statement, the grand scheme of things

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 38:15

Summary:

This video introduces the problem statement that frames the “nonlinear predictive control” developments of video [mpcunic2EN] where actual code will be discussed, over a non-holonomic unicycle robot that can advance or turn.

In here, we discuss the “big picture” of what moving a robot from a start configuration to a goal one means in a cluttered environment. We need:

• Stating the problem correctly as a mathematical optimization problem: start/end configurations (or regions), defining a cost index summarising in one number the application requirements.

• High-level planning (preliminary waypoints, safe corridor)

• Actual numerical optimization, smoothing the preliminary waypoints within the safe corridor

• Analysing the solution (check that we have a feasible solution, and that it is sensible in practice, animations)

• Implementing the solution either in open-loop (just replay the control actions moving from waypoint to waypoint) or closed-loop (two options: either recompute the MPC optimal trajectory or converge to the precomputed one via an error-based control law plus feedforward)

• Dealing with the sim-to-real gap: maps have errors, localization is imprecise, unexpected obstacles (maybe moving ones) must be handled. This can be addressed the hard way, i.e., remapping (SLAM), replanning (spatio-temporal planning if obstacles are moving), or, well, as a simplistic solution, adding a potential field generating an artificial repulsive force from obstacles and hoping that we don’t get stuck in, say, an “U-shaped” passage.

The next videos [mpcunic2EN] and [mpcunic3EN] will provide an in-depth discussion of the optimization code, and video [mpcunic4EN] will discuss simulations and animations of some trajectories, closing the case study.

I acknowledge the collaboration of my colleagues J.L. Pitarch and L. Armesto in drafting the code and providing background and fruitful discussions on the case study.

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