Constrained Optimization for Safe and Visibility-Aware Shared Control of Magnetically Actuated Microrobots

Safe and intuitive telemanipulation of multiple microrobots is limited by visual occlusions that compromise control and task success. This paper introduces a shared control framework that guarantees safety and visibility by formulating the control problem as a constrained optimization problem. Our framework combines Control Lyapunov Functions (CLFs) for operator-driven stability with High-Order Control Barrier Functions (HOCBFs) to enforce collision and occlusion avoidance, all resolved within a real-time Quadratic Program (QP). A key innovation is a rendering technique based on the QP’s Lagrange multipliers, which are used to decompose the optimal control solution. This method isolates the effects of individual constraints to provide the human operator with distinct, interpretable visuohaptic cues for navigation and avoidance. The architecture also includes a viewpoint optimization system with a virtual autonomous camera to maximize task visibility. The framework is validated via two user studies in simulation and a demonstration on a real-world electromagnetic microrobotics actuation system. Results confirm that our visuo-haptic shared control strategies significantly improve user performance and task completion rates, while the control design provably prevents the microrobots from colliding or entering occluded regions.