Data-driven Interpretable Hybrid Robot Dynamics

We study data-driven identification of interpretable hybrid robot dynamics, where an analytical rigid-body dynamics model is complemented by a learned residual torque term. Using symbolic regression and sparse identification of nonlinear dynamics (SINDy), we recover compact closed-form expressions for this residual from joint-space data. In simulation on a 7-DoF Franka arm with known dynamics, these interpretable models accurately recover inertial, Coriolis, gravity, and viscous effects with very small relative error and outperform neural-network baselines in both accuracy and generalization. On real data from a 7-DoF WAM arm, symbolic-regression residuals generalize substantially better than SINDy and neural networks, which tend to overfit, and suggest candidate new closed-form formulations that extend the nominal dynamics model for this robot. Overall, the results indicate that interpretable residual dynamics models provide compact, accurate, and physically meaningful alternatives to black-box function approximators for torque prediction.

💡 Research Summary

This paper, “Data-driven Interpretable Hybrid Robot Dynamics,” presents a novel methodology for creating accurate and interpretable models of robot dynamics by combining first principles with data-driven techniques. The core idea is a hybrid model structure: the total joint torque is expressed as the sum of a known analytical rigid-body dynamics model (τ_rbd) and a data-driven residual term (ε). The research focuses on discovering compact, closed-form mathematical expressions for this residual term using interpretable machine learning methods, specifically symbolic regression and SINDy (Sparse Identification of Nonlinear Dynamics), as opposed to opaque black-box neural networks.

The motivation stems from the limitations of existing approaches. Pure physics-based models often fail to capture complex effects like friction and actuator dynamics, while purely data-driven neural networks, though potentially accurate, lack interpretability, raising concerns for trust and safety in real-world robotics. The proposed hybrid approach seeks the best of both worlds: the generalizability and trust of a physics-based core, augmented by a data-driven correction that is itself understandable.

The paper details two primary methods for learning the residual:

1. Symbolic Regression: This technique searches a vast space of mathematical expressions built from basic operators (+, -, ×, /, etc.) and input variables (joint positions, velocities, accelerations). It optimizes for both accuracy against the data and expression simplicity (complexity), ultimately outputting a human-readable formula for ε.
2. SINDy-inspired Sparse Regression: Adapted for static input-output mapping, this method constructs a large library of candidate nonlinear functions (e.g., polynomials of joint states) and uses sparse regression techniques to find a minimal set of these basis functions whose linear combination best predicts the residual torque.

The experimental validation is conducted in two phases: First, in a simulation environment with a 7-DoF Franka arm whose full dynamics are known, the pipeline is validated. The learned residual models successfully recover the injected unmodeled effects (like viscous friction) with very small relative error. Crucially, these interpretable models outperform standard Multi-Layer Perceptron (MLP) neural network baselines not only in accuracy but, more significantly, in generalization to unseen motion trajectories.

Second, the methods are applied to real-world data collected from a 7-DoF WAM robot arm. The key findings here highlight the practical advantages of interpretability:

• Superior Generalization: Models derived via symbolic regression generalized substantially better to new, out-of-sample trajectories compared to both SINDy and MLP models. The SINDy and MLP models exhibited a strong tendency to overfit the training data.
• Discovery of Candidate Physical Insights: The symbolic regression procedure did not merely fit numbers; it proposed concise closed-form expressions that suggested physically meaningful extensions to the robot’s nominal dynamics model, offering potential explanations for unmodeled behaviors observed in the real hardware.

The paper concludes by discussing the broader implications of such interpretable hybrid models. They can act as “virtual force sensors” for robots lacking expensive physical sensors, enabling large-scale collection of contact-rich data for training vision-language-action models. Furthermore, they can provide physically grounded priors and auxiliary learning signals for reinforcement learning, improving sample efficiency and safety. Overall, the work demonstrates that interpretable, data-driven residual modeling offers a powerful alternative to black-box function approximators, achieving a compelling balance of accuracy, generalizability, and human-understandable insight in robot dynamics identification.