Multi-task closed-loop inverse kinematics stability through semidefinite programming
This addresses stability issues in multi-objective robotic control for applications like humanoid robots or aerial manipulators, representing a novel mathematical development in the field.
The paper tackles the stability problem of hierarchical closed-loop inverse kinematics for highly redundant robots by proposing a method to guarantee system stability through online tuning of control gains using a semidefinite programming formulation with Lyapunov stability conditions. The validity is demonstrated via simulation case studies and a Matlab toolbox.
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.