Source-linked AI summary
Dynamical System-Based Imitation Learning and Neuroadaptive Control for Trajectory Recovery in Autonomous Ships
Yeyson A. Becerra-Mora, José Ángel Acosta
TL;DR
Standard DS-based Imitation Learning can converge globally while losing localized trajectory fidelity under persistent marine disturbances. The paper combines a learned DS reference with a neuroadaptive controller that actively recovers the demonstrated path, and validates this architecture through control-strategy comparisons in the Marine System Simulator toolbox.
Problem
Under large exogenous perturbations, standard DS-based IL prioritizes global target convergence over localized trajectory reproduction fidelity during execution.
Method
A hybrid architecture combines a learned DS-based IL reference generator with an auxiliary neuroadaptive control action for dynamic trajectory recovery.
Results
The framework was validated by comparing different control strategies integrated with DS-based IL in the Marine System Simulator toolbox.
Takeaways & Limitations
Behavioral tracking enables dynamic, human-like corrective responses while the architecture preserves closed-loop stability during disturbance recovery.
Takeaways & Limitations
Trajectory reproduction fidelity can degrade significantly during execution under large exogenous perturbations.
Abstract
from arXiv · showhide
Repetitive maritime operations can be effectively learned using the Imitation Learning (IL) paradigm, which transfers human expertise directly to Unmanned Surface Vehicle (USV) control systems. Dynamical Systems (DS) are widely used to model non-linear human demonstrations while offering inherent stability guarantees. However, real-world execution under persistent marine perturbations reveals a critical trade-off: standard DS-based IL approaches prioritize global target convergence at the expense of localized trajectory reproduction fidelity. To address this limitation, we present a hybrid learning-control architecture that integrates a DS-based IL reference generator with a neuroadaptive controller. Our approach introduces a control action that drives the USV back to the demonstrated path following exogenous disturbances, enabling dynamic human-like reactive alignment-termed behavioral tracking. The proposed methodology is validated using the Marine Systems Simulator (MSS) toolbox. Simulation results confirm that the framework generalizes complex maneuvering tasks while substantially improving trajectory tracking fidelity under disturbances compared to alternative control strategies.
1. Introduction
Imitation Learning transfers human expertise to autonomous systems, while Dynamical Systems provide a way to model complex trajectories and encode stable target convergence. In maritime execution, however, disturbances expose a trade-off between global convergence and faithful local path reproduction, motivating a hybrid neuroadaptive architecture.
- Motivation: Imitation Learning transfers complex, repetitive human tasks to robotic and automated systems through demonstration, learning, and reproduction.In maritime operations, this supports transferring experienced pilots’ maneuvers to onboard ship computers.
- Learning background: Dynamical Systems model complex trajectories in state space, generate motion from arbitrary starting points, and encode task targets as stable attractors.State-dependent DS methods can learn motion dynamics from demonstrations while addressing limitations of time-dependent approaches such as DMPs.
- Challenge: Marine disturbances such as waves, currents, and wind continuously perturb ship trajectories, making precise motion control difficult.Safety- and precision-critical tasks require both recovery to the target and accurate post-disturbance tracking of the intended nominal path.
- Challenge: Standard DS-based IL prioritizes global convergence over localized path reproduction, allowing trajectories to deviate substantially from demonstrations before recovering.Trajectory reproduction fidelity degrades significantly during execution under large exogenous perturbations.
- Proposed approach: The proposed hybrid architecture combines a neuroadaptive controller with a learned DS reference to drive the ship back toward the demonstrated path after disturbances while preserving closed-loop stability.The framework generates dynamic, nonlinear references from demonstrations and uses a Line-of-Sight algorithm to produce heading commands.
- Validation: The study compares different control strategies within DS-based IL and validates the proposed approach in the Marine System Simulator toolbox.The paper presents the comparison as a performance validation of the integrated learning-control framework.
2. Robust learning background
The paper models demonstrations as autonomous dynamical systems learned from data, then integrates Gaussian mixture modeling with Lyapunov-based constraints to obtain stable motion estimates. This offline learning reduces velocity-estimation error while preserving stability, but computational cost grows with model complexity.
- Demonstrations encode point-to-point motions with a shared target and are modeled as autonomous dynamical systems over an open state space.
- A first-principles nonlinear model is assumed unavailable, so GMM learns the dynamics while a control Lyapunov function enforces asymptotic stability.
- GMM parameters describe demonstration data through Gaussian priors, means, and covariances, which are optimized using expectation-maximization and used with GMR to estimate dynamics.The learned estimate weights Gaussian kernels according to their influence on each state.
- The learned control signal is obtained by analytically solving a constrained optimization problem based on a simplified Sontag formula.
- WSAQF provides a suitable control Lyapunov function with a unique global minimum at the target through positive definite matrices and asymmetric shaping vectors.
- The objective reduces velocity-estimation error while preserving stability, but increasing Gaussian kernels or positive definite matrices increases computational time.
- Although offline learning accounts for demonstration noise, an external control action remains necessary to guarantee closed-loop stability during online execution.
3. Nonlinear Adaptive Control for online tracking execution
The proposed online controller combines a learned dynamical-system reference with model-reference neuroadaptive control to track ship motion despite uncertainty and disturbances. Lyapunov analysis establishes bounded tracking and parameter errors, while the learned reference embeds behavioral trajectory information into the adaptive closed loop.
- Adaptive and neuroadaptive control mitigate external noise, system failures, time-varying dynamics, and modeling inaccuracies without requiring highly precise mathematical models.
- The nonlinear plant model represents ship position and velocity while grouping control-effectiveness uncertainty, environmental disturbances, and approximation error into an unstructured uncertainty term.
- The neuroadaptive controller combines nominal and adaptive control laws, with the learned reference entering the reference model that specifies desired closed-loop performance.
- The architecture’s novelty is learning the reference trajectory, unlike standard MRAC architectures that use a predefined reference.
- The adaptive update law uses a learning rate and leakage modification, with leakage preventing parameter estimates from growing unbounded due to drift-causing effects.
- Reducing approximation error or leakage diminishes positive terms, but neural approximation must remain tight over the operating set, creating a convergence-rate versus parameter-drift trade-off.
- Under bounded approximation and weighting errors, the tracking and weight-estimation errors are uniformly ultimately bounded.
- The proof also requires bounded learned reference dynamics; together, bounded reference and error signals imply bounded plant and reference-model states.
4. Validation with realistic simulator
Validation uses a nonlinear container-ship model in the MSS toolbox to learn trajectories and evaluate heading-based control. The neuroadaptive approach achieves the strongest trajectory-tracking performance among the compared controllers, including under noisy maritime disturbances.
- Simulator and ship model: The study validates DS-based imitation learning with a numerical container-ship model in the Marine System Simulator toolbox.The model is used as a benchmark for testing marine control algorithms.
- Simulator and ship model: The container-ship dynamics are simplified by neglecting pitch and heave effects while retaining surge, sway, roll, yaw, and heave-related force and moment modeling.The resulting hydrodynamic forces and moments are expressed through the ship’s nonlinear equations of motion.
- Learning complex trajectories: Three sets of geographically similar nonlinear trajectories are simulated, with distances ranging from 2.59 M to 3.02 M and 5000 recorded data points per learning dataset.Preprocessing reduces the data burden while retaining the recorded trajectory information; five Gaussian kernels and two asymmetric quadratic functions are used.
- Learning complex trajectories: The learned DS reference generalizes demonstrations from nearby initial positions without requiring re-planning or human intervention when the ship’s geographic position changes.Demonstrations and estimated trajectories are distinguished in Fig. 3, with the learned system producing streamlines toward the common target.
- Reference comparison: The learning-based reference lets the ship follow the trajectory smoothly, whereas the demonstration-based reference requires first reaching the demonstration and demands more control effort.Both reference comparisons use the same initial condition and similar targets.
- Trajectory and heading tracking: The neuroadaptive controller provides the best results among the compared controllers, and its trajectory remains closest to the learning-based reference under induced noise.PD and MRAC are used as comparison controllers; heading tracking and SEA results corroborate the neuroadaptive advantage.
5. Conclusions
The study integrates DS-based imitation learning with neuroadaptive control for high-fidelity trajectory tracking under severe marine disturbances. Simulations support superior generalization and tracking fidelity, while practical deployment still requires parameter tuning and future physical-USV validation.
- Conclusions: The two-phase architecture generalizes human maneuvers into state-dependent reference trajectories and adds neuroadaptive control for stable trajectory recovery.The design addresses the trade-off between global convergence and localized path fidelity.
- Conclusions: Comparative evaluations found superior neuroadaptive tracking fidelity over standard control baselines in both low- and high-disturbance regimes.The study also reports superior generalization across diverse initial conditions and three trajectory scenarios.
- Conclusions: Optimal closed-loop performance requires systematic tuning of neuron density, adaptive gains, leakage terms, and hyperparameters.The framework is described as robust to system uncertainties, but its performance remains tuning-sensitive.
- Conclusions: Future work will experimentally deploy the method on a physical USV and add online obstacle avoidance for dynamic threats and marine traffic.These extensions target real-world hydrodynamic effects and more complex operating scenarios.
Appendix A. Nomoto model for MRAC
The appendix uses the first-order Nomoto model as the reference model for MRAC. It treats the time constant and control gain as unknown and maps heading dynamics into state-space variables.
- Appendix A. Nomoto model for MRAC: The first-order Nomoto model serves as the reference model for MRAC.
- Appendix A. Nomoto model for MRAC: The MRAC formulation assumes that the Nomoto parameters T and G are unknown.The passage identifies T as the time constant and G as the control gain.
- Appendix A. Nomoto model for MRAC: The state-space variables are x1 = ψ, x2 = r, and the input is u = uδ.The state and input matrices match those used in the neuroadaptive approach, while uncertainty follows the Nomoto model.