Actuator-Aware Inverse Kinematics with Joint-Limit Admissibility for Torque-Controlled Redundant Robots

Technical Summary: Actuator-Aware Inverse Kinematics with Joint-Limit Admissibility for Torque-Controlled Redundant Robots

Problem Statement
Redundant robots possess more actuated joints than necessary to achieve a specific task-space motion, offering extra degrees of freedom to satisfy secondary objectives like joint-limit avoidance. However, in torque-controlled architectures, the inverse kinematic (IK) output is not the final control input but a reference velocity supplied to a downstream torque-level controller (e.g., Virtual Decomposition Control). Consequently, minimizing the commanded kinematic residual alone does not guarantee good realized motion. If the generated joint-velocity reference is incompatible with the downstream controller's dynamics or actuator limits, the physical system may fail to track the task, particularly near joint limits. Existing IK methods often resolve redundancy based on kinematic criteria (e.g., minimum norm, null-space projection) without explicitly accounting for the compatibility of the reference with the specific torque-level control loop or actuator capacity constraints.

Methodology
The paper proposes a controller-compatible IK formulation that generates joint-level required velocities ($\dot{q}_r$) via a convex quadratic programming (QP) problem. The method is designed to function as an intermediate layer between an endpoint trajectory and a redundant robot's torque-level controller.

1. Controller-Compatibility Objective: The QP minimizes a cost function that balances task preservation with controller compatibility. The weighting matrix ($W_c$) includes:

   • Isotropic Baseline: Ensures well-conditioning.
   • Previous-Command Consistency ($W_\Delta$): Penalizes abrupt changes in the required velocity relative to the previous step, promoting smoothness.
   • Actuator Torque-Capacity Weighting ($W_\tau$): Penalizes the use of joints with lower torque capacity relative to the strongest joint in the system. This weighting is derived from known actuator limits, not measured torque.

2. Joint-Limit Admissibility: Instead of hard constraints that might render the QP infeasible, the method employs Control Barrier Function (CBF)-style inequalities to define an admissible set of required velocities ($D_r(q)$). These bounds ensure that the commanded velocity does not drive the joint too rapidly toward its mechanical limits.

3. Soft Task Constraint: To handle cases where the task command is incompatible with the admissible velocity set, the task equation ($J\dot{q}_r = V_r$) is treated as a soft constraint using a slack variable ($s$). The task residual is penalized in the objective function rather than being the primary minimization target, allowing the solver to prioritize controller compatibility when necessary.

Key Contributions

• Formulation: A novel QP-based IK formulation that explicitly incorporates actuator torque capacity and previous-command consistency into the redundancy resolution for torque-controlled robots.
• Reference-Level Safety: The introduction of CBF-style bounds on the required velocity (the IK output) rather than the plant input, providing reference-level joint-limit admissibility without modifying the downstream controller.
• Task-Admissibility Trade-off: A mechanism to balance task preservation and controller compatibility by using a slack variable for the task equation, preventing the task residual from overriding the need for feasible, smooth references.

Experimental Results
The method was evaluated on a 7-DoF upper-limb exoskeleton using a Virtual Decomposition Control (VDC) framework. It was compared against four baselines: Pseudoinverse (PINV), Damped Least-Squares (DLS), Null-Space Joint-Limit Avoidance (NS-JLA), and a Task-Preserving QP (TP-QP) that uses the same admissibility constraints but lacks the controller-compatibility objective.

• Realized Performance: The proposed method achieved the lowest Root Mean Square (RMS) position and orientation errors, as well as the lowest realized task-velocity residuals, outperforming all baselines. Notably, it reduced RMS position error by 29.6% and RMS orientation error by 20.2% compared to the TP-QP baseline.
• Limit Behavior: The proposed method demonstrated a significantly lower "limit-pushing" index (commands directing motion toward limits), reducing it by up to 96% compared to other methods.
• Torque Efficiency: It resulted in the lowest RMS torque norm, suggesting more efficient use of actuator resources.
• Admissibility: The method maintained zero violations of the admissible required-velocity bounds, whereas kinematic baselines (PINV, DLS, NS-JLA) frequently exceeded these bounds.

Significance and Claims
The paper claims that for torque-controlled redundant robots, IK should not merely minimize kinematic error but must generate joint-level references that are compatible with the downstream controller and actuator capabilities. The results indicate that the proposed formulation achieves a superior balance between task preservation and admissibility. By generating references that respect actuator capacities and avoid aggressive limit-pushing, the method improves realized task behavior without requiring any redesign of the existing torque-level controller. The authors modestly frame these findings as "reference-level joint-limit awareness" and "controller-compatible redundancy resolution," rather than a formal proof of plant-level safety. Future work is identified as investigating coupled IK–torque-control constraint formulations and formal closed-loop constraint analysis.