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Kinodynamic Motion Planning via Funnel Control for Underactuated Unmanned Surface Vehicles

Dženan Lapandić, Christos K. Verginis, Dimos V. Dimarogonas, Bo Wahlberg

TL;DR

This work tackles kinodynamic motion planning for underactuated USVs by marrying a two-layer approach: (i) a higher-level planner that uses RRT and B-splines to generate smooth, collision-free reference trajectories respecting velocity and acceleration limits, and (ii) a lower-level PPC-based controller that enforces prescribed-performance tracking around the reference while accommodating input constraints and actuator saturation. The key novelty lies in extending prescribed performance control to underactuated, saturated USVs and proving stability with bounded signals, alongside an optimization-based trajectory smoothing step that avoids collisions and reduces jerk. The approach is validated through real-world open-water experiments on a Piraya USV, demonstrating robust tracking and safe operation despite disturbances and delays. Collectively, the framework provides a practical, theoretically grounded pipeline for autonomous USV navigation in uncertain, obstacle-rich environments with finite actuation capabilities.

Abstract

We develop an algorithm to control an underactuated unmanned surface vehicle (USV) using kinodynamic motion planning with funnel control (KDF). KDF has two key components: motion planning used to generate trajectories with respect to kinodynamic constraints, and funnel control, also referred to as prescribed performance control, which enables trajectory tracking in the presence of uncertain dynamics and disturbances. We extend prescribed performance control to address the challenges posed by underactuation and control-input saturation present on the USV. The proposed scheme guarantees stability under user-defined prescribed performance functions where model parameters and exogenous disturbances are unknown. Furthermore, we present an optimization problem to obtain smooth, collision-free trajectories while respecting kinodynamic constraints. We deploy the algorithm on a USV and verify its efficiency in real-world open-water experiments.

Kinodynamic Motion Planning via Funnel Control for Underactuated Unmanned Surface Vehicles

TL;DR

This work tackles kinodynamic motion planning for underactuated USVs by marrying a two-layer approach: (i) a higher-level planner that uses RRT and B-splines to generate smooth, collision-free reference trajectories respecting velocity and acceleration limits, and (ii) a lower-level PPC-based controller that enforces prescribed-performance tracking around the reference while accommodating input constraints and actuator saturation. The key novelty lies in extending prescribed performance control to underactuated, saturated USVs and proving stability with bounded signals, alongside an optimization-based trajectory smoothing step that avoids collisions and reduces jerk. The approach is validated through real-world open-water experiments on a Piraya USV, demonstrating robust tracking and safe operation despite disturbances and delays. Collectively, the framework provides a practical, theoretically grounded pipeline for autonomous USV navigation in uncertain, obstacle-rich environments with finite actuation capabilities.

Abstract

We develop an algorithm to control an underactuated unmanned surface vehicle (USV) using kinodynamic motion planning with funnel control (KDF). KDF has two key components: motion planning used to generate trajectories with respect to kinodynamic constraints, and funnel control, also referred to as prescribed performance control, which enables trajectory tracking in the presence of uncertain dynamics and disturbances. We extend prescribed performance control to address the challenges posed by underactuation and control-input saturation present on the USV. The proposed scheme guarantees stability under user-defined prescribed performance functions where model parameters and exogenous disturbances are unknown. Furthermore, we present an optimization problem to obtain smooth, collision-free trajectories while respecting kinodynamic constraints. We deploy the algorithm on a USV and verify its efficiency in real-world open-water experiments.
Paper Structure (14 sections, 1 theorem, 69 equations, 10 figures)

This paper contains 14 sections, 1 theorem, 69 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Main Results
  4. Transformed dynamics
  5. Control Design
  6. PPC on distance error
  7. PPC on forward velocity error
  8. PPC on orientation error
  9. PPC on angular velocity error
  10. Handling input constraints
  11. Stability
  12. Kinodynamic motion-planning
  13. Experimental Results
  14. Conclusion

Key Result

Theorem 1

Consider the transformed USV dynamics eq:model_final under the proposed control scheme eq:first-eq:saturated_thrust. If the following assumptions hold where $\underaccent{\bar{}}{F}_T$ is a positive constant, $\bar{F}_T$ and $\bar{\alpha}_r$ are the input constraints eq:input_constraints, and $\bar{F}_u$ and $\bar{F}_r$ are appropriate positive constants, then it holds that $\rho_{d,\textup{min}}

Figures (10)

  • Figure 1: Piraya autonomous unmanned surface vehicle. Courtesy of https://portal.waraps.org/
  • Figure 2: The control objective is that the error evolves inside the prescribed performance funnel.
  • Figure 3: The considered transformation in NED inertial frame.
  • Figure 4: The convex hull of a set of four consecutive points is linearly separable from the obstacles.
  • Figure 5: The figure shows two runs of the trajectory generation algorithm with RRT and the same setup of obstacles as it will be in the real-world experiments. Two different RRT paths were obtained for comparison. The trajectory is then generated using the optimization problem in Problem \ref{['prob:trajectory_generation']}. Moreover, we show the optimization result without RRT points with $w_1 = 0$ in green. Note that interpolating through the RRT points only as in verginis2022kdf would result in a difficult trajectory to follow with unnecessary deviations as depicted in red.
  • ...and 5 more figures

Theorems & Definitions (6)

  • Theorem 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • proof