Adaptive Nonlinear Model Predictive Control for a Real-World Labyrinth Game

TL;DR

This work tackles real-world labyrinth control by addressing nonlinear, non-convex dynamics and obstacle avoidance. It introduces a two-layer model predictive control framework: a slow high-level solver performs pseudo-global trajectory planning with obstacle constraints, and a fast low-level solver tracks the HL path in real time, aided by a disturbance compensator and a learned feed-forward angle map. Obstacles are modeled with nonlinear inequalities using a superellipse representation, and computational efficiency is achieved via a targeted look-up of nearby obstacles and a short horizon for the LL controller. Experimental results show that the nonlinear, obstacle-aware MPC outperforms cascaded PID and linear MPC in terms of full-path completion and speed, demonstrating robustness to disturbances and model inaccuracies in a real lab setup.

Abstract

We present a nonlinear non-convex model predictive control approach to solving a real-world labyrinth game. We introduce adaptive nonlinear constraints, representing the non-convex obstacles within the labyrinth. Our method splits the computation-heavy optimization problem into two layers; first, a high-level model predictive controller which incorporates the full problem formulation and finds pseudo-global optimal trajectories at a low frequency. Secondly, a low-level model predictive controller that receives a reduced, computationally optimized version of the optimization problem to follow the given high-level path in real-time. Further, a map of the labyrinth surface irregularities is learned. Our controller is able to handle the major disturbances and model inaccuracies encountered on the labyrinth and outperforms other classical control methods.

Figures (11)

• Figure 1: The labyrinth game is a marble game with the goal of steering a ball from a start to an end position while avoiding letting the ball fall down the holes. Pictured above is the BRIO Labyrinth, introduced almost 80 years ago, and with millions sold.
• Figure 2: Hardware setup of the robotic system.
• Figure 3: Schematic representation of a ball-plate-system.
• Figure 4: Schematic representation of the plate-tilting-mechanism
• Figure 5: Concept of the non-linear MPC approach. Blue: Ball. Green star: Current goal. Red: High-level path. Yellow: Low-level path. Purple: Global optimal path around obstacles.