IKLayer: A Differentiable Inverse Kinematics Layer for Whole-Body Control
Abstract
In modern robotics, learning-based policies are increasingly paired with model-based controllers to produce behaviors that are both adaptive and physically feasible. Yet these controllers -which enforce constraints such as kinematic feasibility, joint limits, collision avoidance or balance -are usually treated as non-differentiable black boxes: no gradient flows back through them to the policy learning pipeline. This disconnect prevents gradient-based policy learning from accounting for the physical constraints that actually shape the executed motion: the policy is trained to describe a trajectory rather than to produce one, and compensating for this typically requires large datasets or hand-tuned heuristics. We address this gap by introducing IKLayer, a fully differentiable wholebody layer based on differential inverse kinematics. IKLayer solves a cascade of parametric quadratic programs that encode physical constraints and differentiates through each program via implicit differentiation. To bridge the Euclidean output of neural networks and the SE(3) input poses required by the IK controller, we adopt a differentiable parameterization R 9 → SE(3) and derive its analytic Jacobian, which is free of periodic singularities and produces well-conditioned gradients uniformly over SE(3). On a simulated humanoid reaching task where balance constraints make a single-arm motion infeasible, training through IKLayer discovers a counterweight strategy in minutes, whereas zero-order baselines fail to solve the task. More broadly, these results suggest that exposing a controller's constraints to the policy's gradients turns constraint satisfaction from something the policy must learn into a property of the architecture.
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BibTeX
@misc{scheffler2026iklayer,
title = {{IKLayer: A Differentiable Inverse Kinematics Layer for Whole-Body Control}},
author = {Mathis Scheffler and Yann de Mont-Marin and Cordelia Schmid and Justin Carpentier},
howpublished = {HAL},
year = {2026},
month = oct,
url = {https://hal.science/hal-05778276v1},
note = {CC BY-NC 4.0},
}
RIS
TY - UNPB
TI - IKLayer: A Differentiable Inverse Kinematics Layer for Whole-Body Control
AU - Mathis Scheffler
AU - Yann de Mont-Marin
AU - Cordelia Schmid
AU - Justin Carpentier
PY - 2026
DA - 2026/10/05
PB - HAL
UR - https://hal.science/hal-05778276v1
AB - In modern robotics, learning-based policies are increasingly paired with model-based controllers to produce behaviors that are both adaptive and physically feasible. Yet these controllers -which enforce constraints such as kinematic feasibility, joint limits, collision avoidance or balance -are usually treated as non-differentiable black boxes: no gradient flows back through them to the policy learning pipeline. This disconnect prevents gradient-based policy learning from accounting for the physical constraints that actually shape the executed motion: the policy is trained to describe a trajectory rather than to produce one, and compensating for this typically requires large datasets or hand-tuned heuristics. We address this gap by introducing IKLayer, a fully differentiable wholebody layer based on differential inverse kinematics. IKLayer solves a cascade of parametric quadratic programs that encode physical constraints and differentiates through each program via implicit differentiation. To bridge the Euclidean output of neural networks and the SE(3) input poses required by the IK controller, we adopt a differentiable parameterization R 9 → SE(3) and derive its analytic Jacobian, which is free of periodic singularities and produces well-conditioned gradients uniformly over SE(3). On a simulated humanoid reaching task where balance constraints make a single-arm motion infeasible, training through IKLayer discovers a counterweight strategy in minutes, whereas zero-order baselines fail to solve the task. More broadly, these results suggest that exposing a controller's constraints to the policy's gradients turns constraint satisfaction from something the policy must learn into a property of the architecture.
ER -