Efficient resolution of potentially conflicting linear constraints in robotics

Dimitar Dimitrov (1) , Alexander Sherikov (1) , Pierre-Brice Wieber (1)

1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems

—A classical approach to handling potentially conflicting linear equality and inequality constraints in robotics is to impose a strict prioritization between them. Ensuring that the satisfaction of constraints with lower priority does not impact the satisfaction of constraints with higher priority is routinely done by solving a hierarchical least-squares problem. Such a task prioritization is often considered to be computationally demanding and, as a result, it is often approximated using a standard weighted least-squares problem. The main contribution of this article is to address this misconception and demonstrate, both in theory and in practice, that the hierarchical problem can in fact be solved faster than its weighted counterpart. The proposed approach to efficiently solving hierarchical least-squares problems is based on a novel matrix factorization, to be referred to as " lexicographic QR " , or ℓ-QR in short. We present numerical results based on three representative examples adopted from recent robotics literature which demonstrate that complex hierarchical problems can be tackled in real-time even with limited computational resources.

Domaines: Automatique / Robotique; Analyse numérique [math.NA]

Dimitar Dimitrov, Alexander Sherikov, Pierre-Brice Wieber. Efficient resolution of potentially conflicting linear constraints in robotics. 2015. ⟨hal-01183003⟩