Centered solutions for uncertain linear equations

Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we derive convex representations for united and tolerable solution sets. Secondly, to obtain centered solutions for uncertain linear equations, we develop a new method based on adjustable robust optimization (ARO) techniques to compute the maximum size inscribed convex body (MCB) of the set of the solutions. In general, the obtained MCB is an inner approximation of the solution set, and its center is a potential solution to the system. We use recent results from ARO to characterize for which convex bodies the obtained MCB is optimal. We compare our method both theoretically and numerically with an existing method that minimizes the worst-case violation. Applications to the input–output model, Colley’s Matrix Rankings and Article Influence Scores demonstrate the advantages of the new method

Optimizing Dynamic Trajectories for Robustness to Disturbances Using Polytopic Projections

This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear programming problem is not tractable for state-of-the-art solvers, but it is possible to overcome this complication by exploiting the structure induced by the kinematics of the robot. The non-trivial transcription proposed allows trajectory optimization frameworks to converge to highly robust dynamic solutions. We demonstrate the results of our approach using a quadruped robot equipped with a manipulator.Comment: Final accepted version to the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) 2020. Supplementary video: https://youtu.be/vDesP7IpTh