基于半定规划的多任务闭环逆运动学稳定性
Multi-task closed-loop inverse kinematics stability through semidefinite programming
摘要：
当今复杂的机器人设计在某些情况下包括大量的自由度，使得能够实现多目标任务解决方案（例如，人形机器人或空中操纵器）。本文针对这种高冗余度机器人，研究了分层闭环逆运动学算法的稳定性问题。我们提出了一种方法来保证系统的稳定性，通过执行的闭环控制增益的在线调整。我们定义了一个半定规划问题（SDP），这些收益作为决策变量和离散时间李雅普诺夫稳定性条件作为一个线性矩阵不等式，约束SDP优化问题，并保证优先任务的稳定性。据作者所知，这项工作是第一次数学发展的SDP制定，引入稳定性条件的多目标闭环逆运动学问题的高度冗余机器人。所提出的方法的有效性证明通过模拟案例研究，包括教学的例子和Matlab工具箱，为社会的利益。
英文摘要：
Today's complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the stability problem of a hierarchical losed-loop inverse kinematics algorithm for such highly redundant robots. We present a method to guarantee system stability by performing an online tuning of the closedloop control gains. We define a semi-definite programming problem (SDP) with these gains as decision variables and a discrete-time Lyapunov stability condition as a linear matrix inequality, constraining the SDP optimization problem and guaranteeing the stability of the prioritized tasks. To the best of authors' knowledge, this work represents the first mathematical development of an SDP formulation that introduces stability conditions for a multi-objective closed-loop inverse kinematic problem for highly redundant robots. The validity of the proposed approach is demonstrated through simulation case studies, including didactic examples and a Matlab toolbox for the benefit of the community.
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