A Physics-Informed Collision Learning Framework for Collaborative Robot Motion Generation

Summary

Close-proximity multi-arm manipulation requires collision models that are both geometrically accurate and differentiable enough for real-time optimization.

Abstract Summary

Close-proximity multi-arm manipulation requires collision models that are both geometrically accurate and differentiable enough for real-time optimization. Classical geometry checkers provide reliable distances but are difficult to use inside gradient-based model predictive control, while conservative proxy models can restrict tightly coupled motion. We present PI-UDF, a physics-informed unified differentiable framework for body-to-body collision distance prediction between articulated robots. PI-UDF combines analytical forward kinematics with learnable link-geometry embeddings and a shared residual network to predict pairwise inter-arm distances directly from robot configurations. To improve safety-critical fidelity, we combine quota-driven boundary mining with an asymmetric boundary-crossing penalty that emphasizes false-safe sign errors near the collision boundary. The learned distance field is integrated into nonlinear MPC as a differentiable inter-arm clearance term. We validate the framework on a real dual-Franka platform through high-speed close-proximity 14-DoF dual-arm swapping, sustained single-arm dynamic evasion, and dynamic-evasion planning configurations with frozen, predicted, and target-switching treatments of the moving arm. Hardware experiments and offline Drake/FCL replay show that PI-UDF provides a differentiable inter-arm clearance estimate suitable for closed-loop collision-aware collaborative robot motion generation.

Key Points

Close-proximity multi-arm manipulation requires collision models that are both geometrically accurate and differentiable enough for real-time optimization.
Classical geometry checkers provide reliable distances but are difficult to use inside gradient-based model predictive control, while conservative proxy models can restrict tightly coupled motion.
We present PI-UDF, a physics-informed unified differentiable framework for body-to-body collision distance prediction between articulated robots.
PI-UDF combines analytical forward kinematics with learnable link-geometry embeddings and a shared residual network to predict pairwise inter-arm distances directly from robot configurations.
To improve safety-critical fidelity, we combine quota-driven boundary mining with an asymmetric boundary-crossing penalty that emphasizes false-safe sign errors near the collision boundary.

Physics Informed Unified Collision Learning Framework

Consider a collaborative system comprising two manipulators with joint configurations $q_{1}\in\mathbb{R}^{n_{1}}$ and $q_{2}\in\mathbb{R}^{n_{2}}$. We denote the full dual-arm configuration by $q=[q_{1}^{\top},q_{2}^{\top}]^{\top}\in\mathbb{R}^{n_{1}+n_{2}}$. Let $\mathcal{V}_{r}(q_{r})\subset\mathbb{R}^{3}$ be the workspace volume occupied by robot $r\in\{1,2\}$ at configuration $q_{r}$.

Network Evaluation and Ablation Studies

To rigorously evaluate the proposed framework, we structure our experiments to assess both system-level safety and the underlying architectural choices. As illustrated in Fig. 1 (a), we evaluate PI-UDF on a fixed-cell dual-arm system consisting of two 7-DoF Franka Emika Panda arms with a fixed relative base placement (inter-base offset $1.16\,\mathrm{m}$, opposing orientations $[0,\pi]$ rad).

OPTIMIZATION-BASED Motion PLANNING INTEGRATION

PI-UDF is actually agnostic to the downstream motion generator. In this work, we instantiate it as a differentiable inter-arm clearance term inside nonlinear model predictive control (NMPC).

Compared with reactive velocity-level collision avoidance based on simplified geometric proxies [ 13 ] , the predictive formulation optimizes tracking, regularization, hardware limits, and inter-arm clearance jointly over a finite horizon.

OPTIMIZATION-BASED Motion PLANNING INTEGRATION — A Physics-Informed Collision Learning Framework for Collaborative Robot Motion Generation — ((c)) Closed-loop motion generation

Real-Robot Experiments

Building on the model evaluation and NMPC formulation of Secs. III–IV, we evaluate PI-UDF as a differentiable safety primitive for closed-loop dual-arm hardware control. All experiments are conducted on a dual Franka Emika Panda system with a fixed relative base placement; the two arms share a common workspace and therefore require continuous inter-arm collision reasoning during execution.

Sources and Demonstrations

Figures are reproduced from Cai et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.