On Sensor Switching Visual Servoing

This article investigates dynamical camera switching during visual servoing tasks using multicamera systems considering image-based and position-based Jacobian transpose control schemes. Stability is discussed using a common Lyapunov function assuming ideal target and camera models and multiple Lyapunov functions under parameter perturbations. It is shown that asymptotical stability cannot be achieved for arbitrary switching under parameter perturbations. Therefore, an energy supervised switching scheme is introduced guaranteeing asymptotical stability. The contribution are stable visual servoing strategies which facilitate instantaneous adjustments of control performance and dynamical device switches in case of task requirements or sensor breakdown. keywords: computer vision, visual servoing, switched systems, hybrid systems, stability, robotics Nomenclature s image features σ switching signal K, Kv gains P index set τ torque J set of Jacobians Ji image Jacobian H set of sensors Jt robot Jacobian f vector field h sensor models V Lyapunov function q joint angles Ci,j equipotential lines Z distance in task-space (.)p, (.)q before and after a switch ei, et control errors t time g gravity force τi time period (.) desired value Λ perturbation matrix .̂ estimated value λ focal-length Cq̇ Coriolis-, centripetal torques ̄̃ e average control error M inertia matrix epose control error trajectory W = [X Y Z φθ ψ] relative pose in RPY xpose trajectory W̄ = [X Y Z φX φY φZ ] T relative pose σe standard deviation