Adapting Neural Robot Dynamics on the Fly for Predictive Control

Adapting Neural Robot Dynamics on the Fly for Predictive Control

Motivation and Background

Accurate robot dynamics modeling is paramount for robust model-based predictive control in autonomous mobile platforms. Physics-based (white-box) models often fail to capture real-world complexities stemming from external disturbances, variable payloads, and actuator degradation. Data-driven (black-box) approaches, such as neural network models, offer increased flexibility but typically require extensive off-line datasets and are computationally expensive to adapt on the fly. Classical adaptive control schemes provide real-time compensation for structured model uncertainties but are limited by their parametric representation of disturbances. Recently, meta-learning and low-rank adaptation techniques have emerged for rapid fine-tuning in machine learning, though their deployment in real-time robot dynamics adaptation has been constrained by onboard computational resources.

Methodological Framework

This work proposes an integrated architecture for on-the-fly neural dynamics adaptation and predictive trajectory tracking control, focusing on quadrotor robots subject to abrupt environmental changes (e.g., payload variations). The approach is composed of three principal stages:

• Offline Incremental Dynamics Learning: An MLP is trained to represent an incremental dynamics model $\delta f_\theta$ that predicts the state change rather than the absolute next state. By leveraging quaternion Lie group structure for orientation, this formulation guarantees adherence to physical constraints without explicit enforcement. Input/output normalization and robust loss weighting based on dataset covariance further enhance model stability and generalization.
• Low-Rank Online Parameter Adaptation: Leveraging truncated SVD on network weights, adaptation is restricted to a low-dimensional subspace, updating only the dominant singular vector directions. Second-order Gauss-Newton optimization (via Riccati recursion and a quadratic approximation to the cost-to-go) efficiently computes online parameter updates, incorporating line search and regularization for stability.
• Predictive Model-Based Control: The adapted dynamics model drives a finite-horizon optimal tracking controller using recursive backward pass (DDP-like) updates. The control policy is efficiently solved on-board, and augmented with incremental nonlinear dynamic inversion for robustness during flight.

  Figure 1: Overview of the proposed on-the-fly dynamics learning and predictive control architecture combining offline training and efficient online adaptation.

Model Training and Benchmarking

The model is pre-trained using simulated trajectories from a quadrotor platform. The dataset covers a diverse range of positions, orientations, velocities, and angular velocities, and is normalized to avoid bias from state magnitude.

Figure 2: Distribution of state and velocity features in training and validation sets used for offline neural dynamics model learning.

Windows of length $T=10$ ($0.1\,\mathrm{s}$) are used for sequential rollouts, and multi-step prediction errors are reported. The model achieves a position RMSE of $0.06\,\mathrm{m}$, orientation RMSE of $0.10\,\mathrm{rad}$, linear velocity error of $0.26\,\mathrm{m/s}$, and angular velocity RMSE of $0.40\,\mathrm{rad/s}$ over a $0.5\,\mathrm{s}$ horizon, demonstrating generalization beyond the training window.

Real-Time Adaptation: Experimental Validation

The system is deployed on a resource-constrained quadrotor platform, with embedded CPU-only computation for real-time adaptation and predictive control. An additional payload equal to $35\%$ of the robot's mass is attached to induce model mismatch. Online adaptation is performed using a rank $p=5$ truncation for parameter updates—reducing the tunable subset to about $T=10$0 of the total network weights, allowing for efficient execution within control cycles.

Figure 3: Quadrotor adapting to a 35% payload increase while tracking a reference trajectory.

Adaptation improves position tracking RMSE by 21% (lemniscate trajectory) and 26% (circular trajectory) compared to the non-adaptive model, with heading RMSE remaining comparable since disturbance primarily affects translational dynamics.

Figure 4: Quadrotor tracking performance on lemniscate and circular trajectories with and without online adaptation under a 35% payload increase.

Numerical Results and Claims

The following strong numerical results are reported:

• Position RMSE: $T=10$1 (adapted) vs $T=10$2 (non-adapted) for lemniscate; $T=10$3 (adapted) vs $T=10$4 (non-adapted) for circle trajectory.
• Parameter Efficiency: Fast adaptation is achieved by updating only $T=10$5 of total NN parameters at ranks $T=10$6, with no observed loss of expressivity on real-world tasks.
• Robust Control Performance: Online adaptation allows for rapid compensation of large unmodeled changes, converging to the desired altitude within $T=10$7 post-disturbance.

Bold claims in the paper include:

• The method achieves robust predictive tracking control in novel operational conditions without full retraining or large dataset requirements.
• Low-rank second-order adaptation enables real-time on-board deployment on resource-constrained hardware, circumventing the computational bottleneck of conventional meta-learning.

Practical and Theoretical Implications

Practically, this framework advances onboard adaptive control capabilities for autonomous robots operating under unpredictable structural changes and disturbances, eliminating the need for a priori model specification or expensive full-network retraining. Theoretically, it sets a precedent for combining low-rank adaptation and second-order optimization for state-dependent neural dynamics learning, with implications for scalable adaptive control as neural architectures become more prevalent in robotics.

Further development could extend this architecture to other robot modalities and environments, employing visual and proprioceptive feedback for broader disturbance modeling. The integration with vision-based state estimation may enhance generalization to more complex, unstructured environments. The use of low-rank adaptation underscores the possibility of principled parameter space restriction for efficient fine-tuning in nonlinear systems control.

Conclusion

This paper introduces a highly efficient method for online neural dynamics adaptation and predictive control, combining offline incremental model learning with low-rank second-order parameter updates. The empirical results highlight substantial improvements in quadrotor trajectory tracking under significant model mismatch, with minimal computational overhead and robust safety margins. The proposed approach is likely to impact future adaptive robotics control systems, possibly extending to multi-modal sensor fusion and broader disturbance regimes.