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Robust Motion-Planning for Uncertain Systems with Disturbances using the Invariant-Set Motion-Planner
IEEE Transactions on Automatic Control ( IF 6.8 ) Pub Date : 2020-10-01 , DOI: 10.1109/tac.2020.3008126
Claus Danielson , Karl Berntorp , Avishai Weiss , Stefano Di Cairano

The invariant-set motion planner uses a collection of safe sets to find a collision-free path through an obstacle-filled environment [1]–[4]. This article extends the invariant-set motion planner to systems with persistently varying disturbances and parametric model uncertainty. This is accomplished by replacing the previously used positive invariant sets with robust positive invariant sets. Since the model uncertainty obfuscates the relationship between the invariant sets in the state space, and the references and obstacles in the output space, we reformulate the dynamics in velocity form so that the system output appears directly in the modified system state. Since the persistently varying disturbances will prevent the closed-loop system from converging to the desired reference, we introduce a new robust connection rule where references are connected when the invariant set of one reference contains the minimal volume robust invariant-set of another. In addition, we bound the time required to transition between invariant sets to ensure safety when the obstacles are moving. By parameterizing the invariant sets using a precomputed input-to-state Lyapunov function, we reduce the real-time computational complexity of our motion planner. The robust invariant-set motion planner is demonstrated for an automated highway driving case study.

中文翻译:

使用不变集运动规划器对具有扰动的不确定系统进行鲁棒运动规划

不变集运动规划器使用一组安全集来在充满障碍物的环境中找到无碰撞路径 [1]-[4]。本文将不变集运动规划器扩展到具有持续变化干扰和参数模型不确定性的系统。这是通过用稳健的正不变集替换先前使用的正不变集来实现的。由于模型不确定性混淆了状态空间中的不变集与输出空间中的参考和障碍之间的关系,我们以速度形式重新表述动力学,以便系统输出直接出现在修改后的系统状态中。由于持续变化的干扰会阻止闭环系统收敛到所需的参考,我们引入了一个新的鲁棒连接规则,当一个引用的不变集包含另一个引用的最小体积鲁棒不变量集时,引用被连接。此外,我们限制了在不变集之间转换所需的时间,以确保障碍物移动时的安全性。通过使用预先计算的输入到状态的 Lyapunov 函数参数化不变集,我们降低了运动规划器的实时计算复杂度。强大的不变集运动规划器在自动高速公路驾驶案例研究中得到了证明。通过使用预先计算的输入到状态的 Lyapunov 函数参数化不变集,我们降低了运动规划器的实时计算复杂度。强大的不变集运动规划器在自动高速公路驾驶案例研究中得到了证明。通过使用预先计算的输入到状态的 Lyapunov 函数参数化不变集,我们降低了运动规划器的实时计算复杂度。强大的不变集运动规划器在自动高速公路驾驶案例研究中得到了证明。
更新日期:2020-10-01
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