Abstract We investigate Model Predictive Control (MPC) schemes without stabilizing constraints or costs for the set-point stabilization of holonomic mobile robots. Herein, we ensure closed-loop asymptotic stability using the concept of cost controllability. To this end, we derive a growth bound on the finite-horizon value function in terms of the running costs evaluated at the current state, which is then used to determine a stabilizing prediction horizon. In the discrete-time setting, we additionally show that asymptotic stability holds for the shortest possible prediction horizon. Moreover, we deduce a lower bound on the MPC performance on the infinite horizon. Theoretical results are verified by numerical simulations as well as laboratory experiments of stabilizing a holonomic mobile robot to a reference set point.

中文翻译：

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无终端约束或成本的完整移动机器人模型预测控制

摘要 我们研究了模型预测控制 (MPC) 方案，而无需稳定完整移动机器人的设定点稳定的约束或成本。在这里，我们使用成本可控性的概念来确保闭环渐近稳定性。为此，我们根据当前状态下评估的运行成本推导出有限范围价值函数的增长界限，然后将其用于确定稳定的预测范围。在离散时间设置中，我们还表明渐近稳定性适用于最短的预测范围。此外，我们推断出无限范围内 MPC 性能的下限。理论结果通过数值模拟以及将完整移动机器人稳定到参考设定点的实验室实验进行验证。