Regulation of Nonholonomic Mobile Robots using Model Predictive Control:Set Point Stabilization, Path Following, and Distributed Control

在自主移动机器人的背景下，非线性模型预测控制（MPC）被应用于不同的控制任务，如设定点稳定、轨迹跟踪和路径跟踪。对于这些应用领域，充分稳定条件的问题可以通过附加终端约束和/或成本来解决。由于一旦考虑到障碍物或几个移动机器人，这些额外的（人工）成分就会受到限制，因此避免这些稳定性强制约束具有实际意义。在科学网络中，我们的目标是发展严格的稳定性保证，既不需要终端区域，也不需要终端约束。在这里，我们遵循三个阶段的计划：首先，我们关注连续时间公式的设定点稳定以及各自的采样数据实现。其次，基于得到的结果，我们考虑路径跟随任务，使移动机器人能够绕过静态障碍物。最后，我们研究了一个有多个移动机器人的环境。在这一理论部分的两侧，我们计划实施和测试所提出的MPC方案，并利用模拟和原型测量其性能。拟议的项目将为从事MPC不同方面工作的早期研究人员建立一个合作平台，这将允许确定和促进未来的联合研究项目。

In the context of autonomous mobile robots, the application of nonlinear model predictive control (MPC) has been proposed for different control tasks such as set-point stabilization, trajectory tracking, and path following. For these application areas the question of sufficient stability conditions can be answered with the help of additional terminal constraints and / or costs. Since these additional (artificial) ingredients are restrictive as soon as obstacles or several mobile robots are taken into account, avoiding these stability enforcing constraints is of practical interest. Within the scientific network our goal is to develop rigorous stability guarantees that require neither terminal regions nor terminal constraints. Herein, we follow a three stage program: First, we focus on set point stabilization for continuous time formulations as well as for the respective sampled-data implementations. Secondly, based on the obtained results, we consider path following tasks in order to enable the mobile robots to circumvent static obstacles. And last, we investigate a setting with several mobile robots. Flanking this theoretical part, we plan to implement and test the proposed MPC schemes as well as measure their performance utilizing both simulations and prototypes. The proposed project shall establish a collaboration platform for early stage researchers working on different aspects of MPC, which will allow for identifying and fostering future joint research projects.