This paper introduces a twist decomposition framework for serial manipulators performing lower mobility tasks. Rather than relying on Jacobian null-space projections, the method separates the end-effector twist into task and redundant components using geometrically defined twist projectors. This formulation provides a direct and intuitive distinction between task-relevant and task-irrelevant motions in operational space, enabling a compact inverse kinematics scheme that naturally handles both manipulator and task redundancy.
This paper proposes actuator-aware inverse kinematics for torque-controlled redundant robots under joint-limit constraints. In the considered architecture, the inverse-kinematic output is not merely a purely kinematic joint-velocity command; it is the required joint velocity supplied to a downstream torque-level controller. Therefore, a small commanded task residual may not necessarily improve realized motion. The proposed method formulates a convex quadratic programming problem whose decision variable is the joint-level required velocity. Control barrier function style bounds impose reference-level joint-limit admissibility, while the task equation is handled through a penalized slack variable. Redundancy is resolved using a controller-compatibility objective that accounts for previous-command consistency and actuator torque-capacity weighting. The method is independent of the particular torque-level controller and can serve as an intermediate IK layer between an endpoint trajectory and a redundant robot controller. Experiments on a virtual-decomposition-controlled seven-degree-of-freedom upper-limb exoskeleton compare the method with standard inverse-kinematic baselines and a constrained task-preserving quadratic programming baseline. The results indicate lower limit-pushing commands, bounded admissible required velocities, and improved realized task behavior in the tested trajectory, without modifying the downstream controller.
We propose a workspace-fibered decomposition framework for motion planning in nR planar redundant manipulators operating in cluttered environments. Rather than planning directly in the full n-dimensional configuration space, the method incrementally constructs obstacle-constrained reachable workspaces of lower-dimensional non-redundant sub-chains and recursively lifts them through redundant orientation fibers. This yields a sequence of reduced planning manifolds that preserve branch-consistent reachability structure while avoiding explicit construction of the full configuration-space obstacle geometry. We first establish that, for planar position-only manipulators, the obstacle-constrained reachable workspace induced by the minimal non-redundant sub-chain provides an exact characterization of feasibility with respect to the connected component of the start configuration, enabling early infeasibility detection prior to introducing redundant degrees of freedom (DOF). We then introduce an incremental fiber-lifting procedure that propagates reachable workspace structure through successive redundant links while enforcing local inverse-kinematic branch consistency using Jacobian determinant continuity constraints. The resulting representation admits efficient reduced-space planning directly on recursively-constructed workspace-fiber manifolds. Experimental results on redundant nR planar manipulators demonstrate that the proposed construction preserves collision-free connectivity structure across successive lifting stages while substantially reducing collision checking complexity relative to direct configuration space reasoning.
Dexterous teleoperation via Mixed Reality (MR)-based interfaces offers a scalable paradigm for transferring human manipulation skills to dexterous robot hands. However, conventional retargeting approaches that minimize kinematic dissimilarity (e.g., joint angle or fingertip position error) often fail in contact-rich rotational manipulation, such as cap opening, key turning, and bolt screwing. This failure stems from the embodiment gap: mismatched link lengths, joint axes/limits, and fingertip geometry can cause direct pose imitation to induce tangential fingertip sliding rather than stable object rotation, resulting in screw axis drift, contact slip, and grasp instability. To address this, we propose DexTwist, a functional twist-retargeting framework for MR-based dexterous teleoperation. DexTwist detects a tripod pinch, estimates the operator's intended screw axis and twist magnitude, and applies a real-time residual joint-space refinement that tracks turning progress while regularizing the robot tripod geometry. The refinement minimizes a virtual-object objective defined by turning angle, screw axis consistency, fingertip closure, and tripod stability. Simulation and real-world experiments show that DexTwist improves turning angle tracking and screw axis stability compared with a vector-based retargeting baseline.