Kinematic and Dexterity Analysis for Stable Jacobian-Switching Control of a Real-Time Reconfigurable Robotic Mechanism

Abstract

Abstract. This article presents the internally-hidden linkage (IHL), a novel self-reconfigurable mechanism featuring encapsulated prismatic–revolute (PR) joints. The IHL enables real-time topological adaptation of workspace, dexterity, and degrees-of-freedom (DOF) without manual intervention, crucial for adaptive manufacturing, adaptive locomotion, and search-and-rescue robotics. Reconfiguration occurs via PR coupling, eliminating discrete lock and associated control states while reducing impact exposure and reconfiguration downtime. Unlike metamorphic or self-constraining designs, the IHL avoids bifurcation singularities, achieving continuous reconfiguration. It is analytically demonstrated that the IHL's workspace exceeds that of its conventional PR counterpart. Its reconfigurability is modeled using screw theory-based kinematics, which captures motion during real-time DOF adaptation. Variable DOF arises through prismatic displacement: when the displacement exceeds a design threshold, the encapsulated revolute joint becomes active, increasing mobility; otherwise, it remains concealed in a lower-DOF mode. Offline workspace/dexterity maps (with singularity screening) switch two Jacobians via a binary condition variable, while Jacobian-switching inverse kinematics with power-shaping-signal control runs online in real-time. This provably enables, for the first time, explicit handling of configuration-dependent DOF and mitigation of singularities, while providing asymptotic stability in “free motion” and passivity guarantees when in contact, during arbitrary reconfiguration between distinct modes. Simulation results confirm the IHL's ability to stably switch between three and four DOF while accurately tracking trajectories. This integration of impact-resistant encapsulated joints with continuous reconfigurability establishes a theoretical and control foundation for real-time self-reconfigurable robots.