标题： 带约束松弛的逆最优控制 显示英文标题

标题： Inverse Optimal Control with Constraint Relaxation

摘要： 逆最优控制（IOC）是一种有前景的范式，用于从能力演示者学习和模仿最优控制策略，或通过从一个或多个相应的最优控制序列中估计未知的目标函数来更深入地理解其意图。 在具有安全保持不等式约束的环境中计算演示的估计时，考虑到所选IOC方法中的这些约束是至关重要的，因为它们对最终控制策略有强烈影响。 然而，能够考虑不等式约束的解决方案策略，如逆Karush-Kuhn-Tucker方法，依赖于它们的正确激活和满足；当处理噪声演示时，这是一个限制性假设。 为了解决这个问题，我们利用了精确惩罚函数的概念进行IOC，并展示了估计精度的保持。 考虑到噪声演示，我们随后说明了惩罚函数的使用如何减少未知变量的数量，以及它们的近似如何增强估计方法在多面体约束环境中考虑错误约束激活的能力。 所提出的方法在三种系统中进行了仿真评估，优于传统松弛方法在噪声演示中的表现。 显示英文摘要

摘要： Inverse optimal control (IOC) is a promising paradigm for learning and mimicking optimal control strategies from capable demonstrators, or gaining a deeper understanding of their intentions, by estimating an unknown objective function from one or more corresponding optimal control sequences. When computing estimates from demonstrations in environments with safety-preserving inequality constraints, acknowledging their presence in the chosen IOC method is crucial given their strong influence on the final control strategy. However, solution strategies capable of considering inequality constraints, such as the inverse Karush-Kuhn-Tucker approach, rely on their correct activation and fulfillment; a restrictive assumption when dealing with noisy demonstrations. To overcome this problem, we leverage the concept of exact penalty functions for IOC and show preservation of estimation accuracy. Considering noisy demonstrations, we then illustrate how the usage of penalty functions reduces the number of unknown variables and how their approximations enhance the estimation method's capacity to account for wrong constraint activations within a polytopic-constrained environment. The proposed method is evaluated for three systems in simulation, outperforming traditional relaxation approaches for noisy demonstrations.