Integrated Guidance and Control for Path-Following with Bounded Inputs

Precise motion control of underactuated surface vessels is a crucial task in various maritime applications. In this work, we develop a nonlinear motion control strategy for surface vessels inspired by the pursuit guidance philosophy. Any sufficiently smooth path can be seen as a continuum of virtual targets moving along a specified path, which the pursuer is trying to catch. Contrary to the traditional path-following methods, this work develops an integrated guidance and control approach capable of following any smooth path (unlike the ones composed of a finite number of straight lines and circles). The approach relies on steering the vehicle such that its velocity vector aligns with the line-of-sight (the line joining the moving virtual target and the surface vessel), resulting in a tail-chase scenario. This leads to a path-following behavior. This integrated approach also overcomes the disadvantages inherent in the traditional two-loop-based approaches. Additionally, the proposed work takes into account the asymmetric actuator constraints in the design, which makes the design close to realistic scenarios. Furthermore, the control law has been derived within a nonlinear framework using sliding mode, and thus remains applicable for a wider envelope. The stability of the proposed control strategy is formally proven. Numerical simulations for various specified paths validate the controller’s accurate path-following performance.

💡 Research Summary

The paper addresses the problem of path‑following for under‑actuated unmanned surface vessels (USVs) by developing an integrated guidance‑and‑control (IGC) scheme that directly maps the vehicle’s nonlinear dynamics to control inputs while respecting asymmetric actuator limits. Traditional path‑following methods typically decompose a desired trajectory into straight‑line and circular segments and employ a two‑loop architecture (outer guidance loop providing a desired heading, inner loop tracking that heading). Such approaches rely on a separation of time scales between loops and often ignore realistic actuator saturation, especially the fact that forward and reverse thrust capabilities differ.

Inspired by pursuit‑guidance concepts from interceptor missile literature, the authors model a “virtual target” moving continuously along the prescribed smooth path. The USV is commanded to align its velocity vector with the line‑of‑sight (LOS) to this virtual target, creating a tail‑chase scenario. The relative kinematics are expressed in terms of the range (R) to the target, the LOS angle (\theta), and the heading error (\theta_U = \gamma_U - \theta). The control objective is to drive (\theta_U \to 0), (R \to 0), and (\dot R \to 0), which guarantees convergence to the path and maintenance on it.

The vehicle dynamics are modeled as a three‑degree‑of‑freedom (surge, sway, yaw) nonlinear system that includes added‑mass terms, Coriolis‑centripetal effects, and quadratic damping. Because the USV is under‑actuated, only surge thrust (\tau_u) and yaw torque (\tau_r) are available; sway thrust is absent.

Control design proceeds in two variants:

1. Unconstrained design with post‑hoc saturation – A sliding‑mode controller (SMC) is first synthesized without considering input limits. The sliding surface is chosen as (s = \theta_U + k_R R) (with (k_R>0)). The SMC law guarantees (\dot V = s\dot s \le -\eta|s|) for some (\eta>0), ensuring finite‑time convergence of the sliding surface and thus of the tracking errors. After the law is derived, a conventional saturation block clips the control commands to the physical bounds.

2. Design with asymmetric saturation embedded – The authors adopt an asymmetric actuator‑saturation model previously introduced in their work