基于平方和优化的线缆悬挂欠驱动臂跃机器人鲁棒控制综合与验证
Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization
AI总结：
本文针对线缆悬挂欠驱动臂跃机器人，提出基于简化柔性线缆模型和SDP/SOS优化的时变鲁棒反馈控制方法，实现不确定性下的可靠轨迹跟踪与臂跃运动。
摘要：
线缆悬挂的欠驱动臂跃机器人控制需要一种鲁棒反馈控制设计，以应对动态不确定性、执行器约束和不可测量状态。本文在先前关于最优轨迹生成和时变LQR控制器设计的工作基础上，开发了一种用于柔性线缆上臂跃运动的鲁棒反馈控制。我们提出了一种新颖的简化模型来近似柔性线缆动力学，从而能够在系统中纳入参数化模型不确定性。然后，我们使用半定规划（SDP）和平方和（SOS）优化来综合具有形式化鲁棒性保证的时变反馈控制，以应对系统中的模型不确定性和不可测量状态。通过仿真、硬件实验以及与时变LQR控制器的比较，结果表明所提出的鲁棒控制器能够产生相对较大的鲁棒后向可达集，并且能够在存在参数化模型不确定性、执行器限制和不可观测状态的情况下，可靠地跟踪预生成的最优轨迹并实现期望的臂跃运动。
英文摘要：
Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.
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