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Collective Dynamics and Control for Multiple Unmanned Surface Vessels

Bin Liu, Zhiyong Chen, Hai-Tao Zhang, Xudong Wang, Tao Geng, Housheng Su, Jin Zhao

arXiv:1905.01215v1eess.SYcs.SY

TL;DR

The paper addresses the challenge of testing multi-USV collective control on real water and coordinating collective behavior with vessel dynamics. It develops a two-level distributed controller and tests it on a real multi-USV platform, reporting theoretical surrounding results and successful hardware and software architectures.

  • Problem

    Real-water experiments on USVs were rare, and coordinating collective behavior with vessel dynamics presents a control challenge.

    Source: §I · p. 1

  • Method

    A two-level onboard distributed controller combines a collective multi-USV protocol with lower-level vessel-dynamics control and is tested on a real platform.

    Source: §I · p. 2, §VII · p. 7

  • Results

    Theorem 1 states that, with exponentially vanishing regulation error and the specified controller, closed-loop states are bounded and the target is asymptotically surrounded.

    Source: A. Asymptotically Surrounding Control · p. 4

  • Takeaways & Limitations

    Experiments on the real multi-USV platform verified the success of the developed hardware and software architectures.

    Source: §VII · p. 7

    The theoretical framework does not accommodate external disturbance, and high-speed operation remains future work.

    Source: §VII · pp. 7–8

Abstract

from arXiv · show

A multi-unmanned surface vessel (USV) formation control system is established on a novel platform composed of three 1.2 meter-long hydraulic jet propulsion surface vessels, a differential GPS reference station, and inter-vessel Zigbee communication modules. The system is also equipped with an upper level collective multi-USV protocol and a lower level vessel dynamics controller. The system is capable of chasing and surrounding a target vessel. The results are supported by rigorous theoretical analysis in terms of asymptotical surrounding behavior and trajectory regulation. Extensive experiments are conducted to demonstrate the effectiveness and efficiency of the proposed hardware and software architectures.

I. INTRODUCTION

The paper distinguishes target-surrounding control from earlier formation tasks and addresses the challenge of coordinating collective behavior with vessel dynamics. It also tests the design on a real multi-USV platform.

I. INTRODUCTION

  • Multi-USV formations can perform complex tasks, and another vessel can replace or rescue a malfunctioning USV in harsh marine environments.The introduction contrasts this with the greater vulnerability of a single USV.Source: §I · p. 1
  • Unlike prior formation-control work, the paper aims to surround a target within the vessels’ convex hull without requiring an initial placement or predefined stand-off distance.Source: §I · p. 1
  • A central challenge is coordinating an upper-level collective protocol with lower-level vessel dynamics while achieving collective behavior and exponentially eliminating trajectory-regulation error.Source: §I · p. 1
  • The authors test their design on a lake-based platform of three 1.2-meter jet-propelled USVs equipped with differential GPS receivers and imaging-processing modules.The introduction notes that real-water experimental results had largely focused on single USVs.Source: §I · pp. 1–2

II. MODELING

The modeling section represents vessel positions and kinematics, then uses a simplified dynamics model intended to support control design and experimental identification. Its dynamics equations retain selected cross nonlinearities for vessels operating at medium speed.

II. MODELING

  • The system models N ≥ 3 vessels by their Cartesian positions and uses the convex hull of those positions to characterize the group’s spatial extent.The supplied text defines the distance from a point to the convex hull and states that it is zero when the point lies within the hull.Source: §II · p. 2
  • The vessel kinematics model uses surge speed w_i, yaw angle ψ_i, sway speed v_i, and yaw rate r_i.Source: §II · p. 2, Figure 1 · p. 2
  • For medium-speed operation (1–3 m/s), the dynamics model retains the cross nonlinearities v_i r_i and w_i r_i while simplifying higher-order nonlinearities.The authors say the simplification is based on experiments and data matching, and seek equations suitable for control and experimental identification.Source: §II · p. 2

III. PROBLEM FORMULATION AND CONTROLLER FRAMEWORK

The section formulates surrounding and equally surrounding behaviors and frames control as an upper-level collective protocol followed by lower-level vessel-dynamics control. It distinguishes Cartesian and polar approaches and specifies the desired behavior under vanishing perturbations.

III. PROBLEM FORMULATION AND CONTROLLER FRAMEWORK

  • The control framework has two levels: an upper-level protocol selects desired vessel signals for collective behavior, and lower-level actuator inputs regulate vessel dynamics to track them.The stated objective is that the closed-loop system achieves the collective behavior when both steps are solved.Source: §III · p. 2
  • The paper studies surrounding and equally surrounding, with the latter requiring a common target distance and minimum pairwise vessel separation.The supplied definition gives d = 2ρ_o sin(π/N) and states that adjacent vessels reach that separation.Source: §III · p. 3
  • Two approaches—Cartesian and polar coordinates—are proposed to realize collective behaviors with different features.Source: §III · p. 3
  • The Cartesian approach designs desired signals so the target is asymptotically surrounded despite a perturbation approaching zero; the polar approach targets equal surrounding under vanishing perturbations.For the polar approach, the formulation also requires each vessel’s radius to remain asymptotically bounded below by a positive constant.Source: §III · p. 3

IV. COLLECTIVE CONTROL DESIGN

This section’s stated objective is to design a controller for each vessel that achieves the specified asymptotically surrounding formation.

IV. COLLECTIVE CONTROL DESIGN

  • The section aims to design a controller for each vessel to achieve the specified asymptotically surrounding formation.Source: §IV · p. 3

A. Asymptotically Surrounding Control

The control objective is to asymptotically surround a specified target position despite perturbations that approach zero. The section gives boundedness and surrounding results for both shared-target and decentralized-estimation settings.

A. Asymptotically Surrounding Control

  • The controller defines communication neighbors as vessels within distance μ and uses the relative position xij = xi − xj.The target-relative position is denoted xoi = xo − xi.Source: A. Asymptotically Surrounding Control · pp. 3–4
  • With exponentially vanishing perturbations, controller (14) keeps the closed-loop states bounded and asymptotically surrounds the target position.The result assumes positive gains γ1 and γ2.Source: A. Asymptotically Surrounding Control · p. 4
  • The proof establishes bounded state and convergence of the mean vessel position to the target position, implying the stated surrounding property.The bounded-state argument precedes the mean-position convergence result.Source: A. Asymptotically Surrounding Control · p. 4
  • When not every vessel can access the target position, a decentralized estimator supports surrounding if the communication network is connected and at least one vessel detects the target.Under these conditions, controller (16) and (17) yields bounded states and asymptotic surrounding, with exponentially convergent target estimates.Source: A. Asymptotically Surrounding Control · p. 4

B. Asymptotically Equally Surrounding Control

The controller drives the vessels toward a specified-radius circle and adjusts their angles to achieve asymptotically equal surrounding. The analysis establishes convergence under vanishing perturbations and identifies a repulsion-based collision-avoidance mechanism, while leaving rigorous collision-avoidance analysis for future work.

B. Asymptotically Equally Surrounding Control

  • The design drives vessels toward a circle of specified radius ρ > 0 and adjusts their angles along the negative gradient of a potential function.The angular design uses the potential function P_o(θ_ij).Source: B. Asymptotically Equally Surrounding… · p. 5
  • The target is asymptotically equally surrounded as the angular perturbation vanishes exponentially, with each vessel’s radius converging to ρ_o.The theorem states the equal-surrounding result is equivalent to the radius condition in (21).Source: B. Asymptotically Equally Surrounding… · p. 5
  • The proof establishes angular phase spacing using a bounded, monotonic potential argument and Barbalat’s lemma.It concludes that adjacent-vessel angle differences approach 2π/N, while other differences are at least 2π/N.Source: B. Asymptotically Equally Surrounding… · p. 5
  • Closer vessels receive larger repulsive angular velocity, providing a follower-collision avoidance mechanism, though rigorous collision-avoidance analysis remains future work.The controller also includes a repulsive velocity between vessels based on their separation.Source: B. Asymptotically Equally Surrounding… · p. 5

V. TRAJECTORY REGULATION

The section designs actuator inputs for the vessel dynamics to track desired motion signals. It states that regulation error converges exponentially when the desired sway velocity is bounded, and notes that the simplified controllers have PI and PD forms in low-frequency motion.

V. TRAJECTORY REGULATION

  • The vessel dynamics are under-actuated: actuator inputs control forward speed and yaw, but not sway velocity directly.The desired sway velocity can be selected subject to the stated condition in the section.Source: §V · p. 5
  • In the investigated scenario, sway velocity is typically small; a vessel can be intervened to reduce it if a large value occurs.The passage describes large sway as a rare situation.Source: §V · p. 5
  • If the desired sway velocity v^r_i is bounded, the actuator controller drives regulation error e_i to zero exponentially.The vessel model is under-actuated: sway velocity cannot be directly controlled.Source: §V · pp. 5–6
  • In low-frequency motion, the simplified propeller-speed and steering controllers have PI and PD forms, respectively.The passage specifies proper feedforward compensation for the PI controller.Source: §V · p. 6

VI. EXPERIMENTS

Experiments validate model identification and single-vessel control before demonstrating collective target capture with the two-level controller. The vessels surround the target at the desired distances and evenly spaced phases.

Experimental platform

  • The experimental platform comprised three HUST-12 vessels, a target vessel, differential GPS, and a wireless LAN hub.Each HUST-12 has an onboard GPS receiver, wireless sensor, embedded controller, motor driver, waterjet propeller, and rudder.Source: §VI · p. 6

Model identification

  • Identification RMSEs for surge, sway, and yaw velocity were less than 5%.Data were sampled every 0.2 s on the experimental platform.Source: §VI · p. 7, Figure 3 · p. 7

Single-vessel control

  • Single-vessel speed and orientation control had overshoot/settling times of 2%/10s and 1%/15s, respectively.The setpoints were 200 cm/s and 300°; the reported performance met the collective-surrounding control requirements.Source: §VI · p. 7, Figure 4 · p. 7

Collective surrounding

  • By 160 seconds, the USVs had captured and surrounded the target; their distances converged to ρ0 and their inter-USV phases to 120°.The experiment began with randomly distributed USVs on a 40 × 40 m² water surface; they caught the target within 50 seconds.Source: §VI · p. 7

VII. CONCLUSIONS

The paper reports a real-platform test of its two-level onboard distributed surrounding controller and successful target capture with evenly spaced vessels. The framework remains bounded by its disturbance assumptions and medium-speed platform.

Conclusion

  • The two-level controller was tested on a real multi-USV platform, where the vessels captured and surrounded the target with phases converging to 120°.The conclusion reports that the tests verified the developed hardware and software architectures.Source: §VII · p. 7, Figure 5 · p. 8, Figure 6 · p. 8
  • The theoretical framework does not accommodate external disturbances; disturbance rejection is future work for more severe environments.Experiments assessed the current scenario as sufficiently satisfactory despite this scope boundary.Source: §VII · p. 7
  • The platform was developed for medium-speed operation (1–3 m/s); high-speed operation (8–10 m/s), including significant communication packet loss issues, remains future work.Source: §VII · p. 8
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