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AD-NODE: Adaptive Dynamics Learning with Neural ODEs for Mobile Robots Control

Shao-Yi Yu, Jen-Wei Wang, Maya Horii, Vikas Garg, Tarek Zohdi

TL;DR

AD-NODE introduces a continuous-time adaptive dynamics model for mobile robots by uniting Neural ODEs with an environment latent encoder and a two-phase training regime. Phase 1 leverages privileged environmental information to learn state evolution, while Phase 2 reconstructs latent environment from history to adapt during deployment, complemented by online MPPI-based control and fine-tuning. The approach outperforms context-aware and other baselines in both simulation and real-world tests across differential-drive and quadrotor platforms, demonstrating robust navigation under spatial and temporal environmental variations. This framework enables long-horizon, adaptive control with model-based planning, offering practical gains for robust autonomous operation in uncertain, partially observable environments.

Abstract

Mobile robots, such as ground vehicles and quadrotors, are becoming increasingly important in various fields, from logistics to agriculture, where they automate processes in environments that are difficult to access for humans. However, to perform effectively in uncertain environments using model-based controllers, these systems require dynamics models capable of responding to environmental variations, especially when direct access to environmental information is limited. To enable such adaptivity and facilitate integration with model predictive control, we propose an adaptive dynamics model which bypasses the need for direct environmental knowledge by inferring operational environments from state-action history. The dynamics model is based on neural ordinary equations, and a two-phase training procedure is used to learn latent environment representations. We demonstrate the effectiveness of our approach through goal-reaching and path-tracking tasks on three robotic platforms of increasing complexity: a 2D differential wheeled robot with changing wheel contact conditions, a 3D quadrotor in variational wind fields, and the Sphero BOLT robot under two contact conditions for real-world deployment. Empirical results corroborate that our method can handle temporally and spatially varying environmental changes in both simulation and real-world systems.

AD-NODE: Adaptive Dynamics Learning with Neural ODEs for Mobile Robots Control

TL;DR

AD-NODE introduces a continuous-time adaptive dynamics model for mobile robots by uniting Neural ODEs with an environment latent encoder and a two-phase training regime. Phase 1 leverages privileged environmental information to learn state evolution, while Phase 2 reconstructs latent environment from history to adapt during deployment, complemented by online MPPI-based control and fine-tuning. The approach outperforms context-aware and other baselines in both simulation and real-world tests across differential-drive and quadrotor platforms, demonstrating robust navigation under spatial and temporal environmental variations. This framework enables long-horizon, adaptive control with model-based planning, offering practical gains for robust autonomous operation in uncertain, partially observable environments.

Abstract

Mobile robots, such as ground vehicles and quadrotors, are becoming increasingly important in various fields, from logistics to agriculture, where they automate processes in environments that are difficult to access for humans. However, to perform effectively in uncertain environments using model-based controllers, these systems require dynamics models capable of responding to environmental variations, especially when direct access to environmental information is limited. To enable such adaptivity and facilitate integration with model predictive control, we propose an adaptive dynamics model which bypasses the need for direct environmental knowledge by inferring operational environments from state-action history. The dynamics model is based on neural ordinary equations, and a two-phase training procedure is used to learn latent environment representations. We demonstrate the effectiveness of our approach through goal-reaching and path-tracking tasks on three robotic platforms of increasing complexity: a 2D differential wheeled robot with changing wheel contact conditions, a 3D quadrotor in variational wind fields, and the Sphero BOLT robot under two contact conditions for real-world deployment. Empirical results corroborate that our method can handle temporally and spatially varying environmental changes in both simulation and real-world systems.

Paper Structure

This paper contains 50 sections, 5 theorems, 43 equations, 7 figures, 7 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Contribution
  3. Related Work
  4. Problem Statement
  5. Adaptive Dynamics Model with NODE
  6. Two-Phase Framework for Learning Adaptive Dynamics
  7. Sampling-Based Control with Online Dynamics Learning
  8. Additional Training Details
  9. Simulation Experiments
  10. Baseline Methods
  11. Data Collection
  12. 2D Differential Wheeled Robot Navigation
  13. Setup
  14. Target tasks
  15. MPC performance
  16. ...and 35 more sections

Key Result

Lemma A.1

Consider the true continuous-time dynamics and the approximate continuous-time dynamics where $f,\hat{f} : \mathbb{R}^d \times \mathcal{U} \to \mathbb{R}^d$, $f$ is Lipschitz continuous in $x$ with Lipschitz constant $L$ and let the approximation error be Based on $\delta(0)=0$, the trajectory error $\delta(t) = \| x(t) - \hat{x}(t) \|$ satisfies the bound Proof. Let $e(t) = x(t) - \hat{x}(t)

Figures (7)

  • Figure 1: (a) Our adaptive dynamics model outperforms CaDM context_aware when combined with MPC in goal-reaching and path-tracking tasks across (top row) differential wheeled robot and (bottom row) quadrotor navigation platforms. Our method works well in unknown environments (such as different layouts of surface textures and wind fields) and accurately reaches the targets, while CaDM struggles with oscillations around the targets. (b) Physical setup of a Sphero BOLT robot navigating through different textures and reaching the goal.
  • Figure 2: (a) Proposed control framework for mobile robots, where MPC is adopted to determine optimal control actions by predicting future trajectories with our proposed dynamics model (AD-NODE). (b) Structure of AD-NODE: the state net models the derivatives of states evolution, the environmental encoder processes privileged information, and the adaptive module reconstructs a latent environmental vector from historical state-action data by regressing to the corresponding latent vector from Phase 1. State prediction is obtained through numerical integration of the dynamics function. Models with trainable weights are indicated with dashed lines.
  • Figure 3: Environment setup for (a) 2D differential wheeled robot and (b) 3D quadrotor.
  • Figure 4: (a) Environment setup for the real-world platform. (b) Examples of friction layouts.
  • Figure 5: The influence of environmental factors on differential wheeled robots and quadrotors under identical control inputs: (a) It is more difficult for a differential wheeled robot to navigate on a slippery surface compared to a non-slippery one. (b) Even when thrust is applied to a quadrotor, strong wind can significantly alter its dynamics, causing it to drift in the x-direction.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Lemma A.1: Error propagation for vector-field models (NODE)
  • Lemma A.2: Error propagation for discrete-time map models (MLP)
  • Lemma A.3: Predicted vs actual finite-horizon cost difference
  • Lemma A.4: Descent inequality for the MPC value function
  • Lemma A.5: Uniformly Ultimate Boundedness