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.

翻译：我们提出了一种非线性非凸模型预测控制方法，用于解决现实世界中的迷宫游戏。我们引入了自适应非线性约束，以表征迷宫内的非凸障碍物。该方法将计算量大的优化问题分为两层：首先，高层模型预测控制器整合完整问题表述，以低频率寻找伪全局最优轨迹；其次，低层模型预测控制器接收经过计算优化的精简版优化问题，实时跟随高层路径。此外，我们学习构建了迷宫表面不规则性地图。该控制器能够处理迷宫中遇到的主要扰动和模型误差，其性能优于其他经典控制方法。