LiftEqui: Lift-Equivariant Kinematic Coordination and Priority-Aware Arbitration for a Shared-Lift Bimanual Robot

This paper presents LiftEqui, a framework that coordinates a follower-only prismatic lift shared by two serial manipulators in leader–follower bimanual teleoperation. Upon bilateral detection, LiftEqui freezes the robot state and utilizes a re-linearized compensation quadratic program (QP) to predict both arm postures across candidate heights, which are screened by joint, singularity, clearance, and residual guards. Height evidence is supplied by kinematic risk (K) and task height (G), while effort utilization (I) reweights arm protection; a smooth minimax objective then selects a single lift target without requiring replanning. The proposed framework was evaluated across 540 grasp-and-place trials. In conflicting scenarios where one arm preferred raising the lift and the other preferred lowering it, worst-arm arbitration (with effort priority disabled) significantly reduced the median post-lift worst-arm cost to 0.417, outperforming mean aggregation (0.500), task-height tracking (0.491), and manipulability maximization (0.527) (p<0.001, Holm-adjusted). Conversely, when both arms shared the same directional preference, the performance did not differ statistically from mean aggregation or task-height tracking. Under 1.0 and 1.5 kg loads, enabling the effort priority shifted the selected height toward the loaded arm in 69 out of 79 blocks where a height transition occurred. This priority effectively decreased the loaded-arm cost from 0.300 to 0.241, while inherently increasing both the unloaded-arm and worst-arm costs. Finally, in a separate per-arm sweep, executing the predicted compensation constrained the measured hand drift to within 20 mm across all 48 runs, achieving a median planning time of 1.59 s.