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arxiv: 1907.02696 · v1 · pith:JXCBW7YNnew · submitted 2019-07-05 · 📡 eess.SY · cs.RO· cs.SY· math.OC

Warm-Started Optimized Trajectory Planning for ASVs

Glenn Bitar , Vegard N. Vestad , Anastasios M. Lekkas , Morten Breivik This is my paper

Pith reviewed 2026-05-25 02:32 UTC · model grok-4.3

classification 📡 eess.SY cs.ROcs.SYmath.OC
keywords trajectory planningautonomous surface vehiclesA* algorithmoptimal controlwarm-startingASVpath planningunderactuated dynamics
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The pith

Warm-starting an optimal control planner with an A*-generated path reduces planning time for ASVs while producing dynamically feasible trajectories.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that an A* algorithm can quickly generate the shortest piecewise-linear path on a decomposed map, after which dynamic information is attached to create an initial guess. This guess warm-starts a nonlinear optimal control planner that uses a 3-degree-of-freedom underactuated ASV model and an objective favoring energy-efficient and observable maneuvers. The warm-start greatly shortens the solver's runtime and yields a trajectory that satisfies the vehicle's dynamics and is locally optimal. A reader would care because ASV operations require planning methods that balance speed, feasibility, and efficiency under motion constraints.

Core claim

The A* algorithm finds the shortest piecewise linear path to the goal, dynamic information is constructed and added to this path to supply an initial guess, and the optimal control-based planner is warm-started with this guess to output a dynamically feasible and locally optimal trajectory in greatly reduced time.

What carries the argument

The warm-start initial guess formed by attaching dynamic information to the A*-generated piecewise-linear path.

If this is right

  • The optimal control planner produces trajectories that respect the nonlinear 3DOF underactuated ASV dynamics.
  • The resulting trajectories are locally optimal with respect to the chosen energy-efficiency and observability objective.
  • Overall planning time drops because the warm-start shortens the solver's search.
  • The A* component always supplies a shortest piecewise-linear path on the uniformly decomposed map before optimization begins.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same warm-start construction could be tested on maps with moving obstacles to check whether replanning remains fast.
  • Similar dynamic augmentation of grid paths might transfer to trajectory planning for other underactuated vehicles.
  • Measuring the distance between the A* guess and the final optimized trajectory could quantify how much the initial guess influences local optimality.

Load-bearing premise

The dynamic information attached to the A* path creates an initial guess close enough to a feasible solution for the optimal control solver to converge reliably.

What would settle it

Running the optimal control planner on the same ASV problems both with and without the A*-derived initial guess and measuring whether convergence fails or runtime increases substantially without it.

Figures

Figures reproduced from arXiv: 1907.02696 by Anastasios M. Lekkas, Glenn Bitar, Morten Breivik, Vegard N. Vestad.

Figure 1
Figure 1. Figure 1: Categorization of some planning algorithms. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Pipelined path planning concept. cases and are generally unpractical. Approximate methods such as e.g. pseudospectral optimal control (Bitar et al., 2018; Ross and Karpenko, 2012) are highly sensitive to initial guesses of the solution and will converge to a local optimum close to this guess. Without a good initial guess, they also experience long run times and are sensitive to problem dimensionality. Zhan… view at source ↗
Figure 3
Figure 3. Figure 3: Map showing the scenario used for planning, with multiple elliptical obstacle [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cost functional development along both the optimized trajectory and the [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: From the heading angle plot, we see that [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 5
Figure 5. Figure 5: State values for heading, velocities and yaw rate for both the optimized [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Zoomed-in section of Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
read the original abstract

We consider warm-started optimized trajectory planning for autonomous surface vehicles (ASVs) by combining the advantages of two types of planners: an A* implementation that quickly finds the shortest piecewise linear path, and an optimal control-based trajectory planner. A nonlinear 3-degree-of-freedom underactuated model of an ASV is considered, along with an objective functional that promotes energy-efficient and readily observable maneuvers. The A* algorithm is guaranteed to find the shortest piecewise linear path to the goal position based on a uniformly decomposed map. Dynamic information is constructed and added to the A*-generated path, and provides an initial guess for warm starting the optimal control-based planner. The run time for the optimal control planner is greatly reduced by this initial guess and outputs a dynamically feasible and locally optimal trajectory.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes combining an A* planner, which finds the shortest piecewise-linear path on a uniform grid, with an optimal-control trajectory planner for ASVs. Dynamic information is attached to the A* path to create an initial guess that warm-starts the optimal-control solver. The resulting trajectories are claimed to be dynamically feasible and locally optimal for a nonlinear 3DOF underactuated ASV model whose objective promotes energy-efficient, observable maneuvers, while greatly reducing the optimal-control solver runtime.

Significance. If the warm-start reliably produces convergence, the hybrid method would offer a practical way to obtain energy-efficient trajectories faster than pure optimal control while retaining local optimality guarantees. The reliance on standard A* completeness and optimal-control formulations is a methodological strength, but the absence of any quantitative runtime data, convergence statistics, or comparison against cold-start baselines limits assessment of practical impact.

major comments (2)
  1. [Abstract] Abstract (warm-start paragraph): The central claim that 'Dynamic information is constructed and added to the A*-generated path' supplies an initial guess 'sufficiently close' for the optimal-control solver to converge reliably to a locally optimal, dynamically feasible trajectory is load-bearing yet unsupported. No construction details, distance metric to the feasible set, or analysis is given showing that a geometrically shortest path remains close under the nonlinear underactuated dynamics and energy objective; the two criteria can diverge on turning radius or speed profiles.
  2. [Abstract] Abstract: The statement that 'the run time for the optimal control planner is greatly reduced' and 'outputs a dynamically feasible and locally optimal trajectory' is presented without any numerical results, success-rate data, or comparison tables. This prevents verification of the claimed improvement and leaves the soundness of the hybrid planner unassessable from the manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (warm-start paragraph): The central claim that 'Dynamic information is constructed and added to the A*-generated path' supplies an initial guess 'sufficiently close' for the optimal-control solver to converge reliably to a locally optimal, dynamically feasible trajectory is load-bearing yet unsupported. No construction details, distance metric to the feasible set, or analysis is given showing that a geometrically shortest path remains close under the nonlinear underactuated dynamics and energy objective; the two criteria can diverge on turning radius or speed profiles.

    Authors: We agree the abstract is too concise to convey the construction process. Section 3 of the manuscript details how velocity and heading profiles consistent with the 3DOF ASV dynamics are interpolated onto the A* path to form the initial guess. We will revise the abstract to include a brief description of this attachment step. On closeness to the feasible set, the work relies on empirical validation across scenarios where the warm-start enables convergence; a formal distance metric or proof under the energy objective is not provided, as it lies beyond the paper's scope. We will add a clarifying sentence noting the empirical basis. revision: partial

  2. Referee: [Abstract] Abstract: The statement that 'the run time for the optimal control planner is greatly reduced' and 'outputs a dynamically feasible and locally optimal trajectory' is presented without any numerical results, success-rate data, or comparison tables. This prevents verification of the claimed improvement and leaves the soundness of the hybrid planner unassessable from the manuscript.

    Authors: We agree that the abstract and manuscript would benefit from explicit quantitative support. The current version emphasizes the method but lacks runtime tables or success rates. We will revise by adding summary statistics (e.g., observed solver time reductions and convergence rates from simulations) to the abstract and expand the results section with cold-start comparisons. revision: yes

Circularity Check

0 steps flagged

No circularity: standard algorithmic combination with no self-referential reductions

full rationale

The paper presents a practical hybrid planner: A* generates a shortest piecewise-linear path on a grid (standard guarantee), dynamic information is attached to form an initial guess, and this warm-starts a nonlinear optimal-control solver. No equations, parameters, or uniqueness claims are shown to reduce by construction to fitted inputs or prior self-citations. The runtime-reduction claim is an empirical outcome of the solver, not a tautological re-statement of the inputs. The skeptic concern addresses empirical reliability of the initial guess under the energy objective, which is a correctness question outside the circularity criteria.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Ledger constructed from abstract only; full paper may contain additional modeling assumptions or parameters.

axioms (2)
  • standard math A* finds the shortest piecewise linear path on a uniformly decomposed map
    Stated as guaranteed in the abstract.
  • domain assumption ASV dynamics are captured by a nonlinear 3DOF underactuated model
    Basis for the optimal-control stage.

pith-pipeline@v0.9.0 · 5677 in / 1172 out tokens · 31030 ms · 2026-05-25T02:32:49.029014+00:00 · methodology

discussion (0)

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Reference graph

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