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Clarity-Driven Adaptive Mission Planning for a Solar-Powered Autonomous Surface Vessel

Kavin M. Govindarajan, Kaleb Ben Naveed, David Li, Devansh R. Agrawal, Mary Maceda, Matthew Bryant, Dimitra Panagou, Chris Vermillion

arXiv:2610.20871v1cs.ROcs.SYeess.SY

TL;DR

Adaptive missions must gather useful scientific information under limited energy while accounting for changing information and battery states. This paper combines online clarity-map adaptation with clarity-driven ergodic planning and SOC-based speed control, and reports simulations and field experiments that direct sensing toward scientifically relevant conditions.

  • Problem

    Adaptive planning must maximize useful scientific information under limited energy while accounting for evolving information fields and battery state, whereas existing approaches often simplify energy constraints and assume non-decaying information.

    Source: §I · pp. 1–2

  • Method

    The framework uses STGPKF estimates to update actual and target clarity maps online, then combines clarity-driven ergodic planning with SOC-based speed control.

    Source: §I · p. 2

  • Results

    Simulations and Jordan Lake field experiments demonstrate that the framework operates as an integrated system and directs sensing toward scientifically relevant conditions.

    Source: §VI · p. 13

  • Takeaways & Limitations

    In the reported simulations, target-directed sampling, spatial clarity, and full-field reconstruction are distinct objectives whose balance depends on selectivity, planner choice, and environmental structure.

    Source: E. Discussion · p. 10, §VI · p. 13

Abstract

from arXiv · show

This paper presents a comprehensive methodology, backed by simulation and experimental results, for an adaptive mission planning strategy that is mathematically grounded in the maximization of the information-driven quantity of clarity. In particular, the methodology introduced in this work addresses the use of sustainably powered autonomous surface vessels (ASVs) to perform scientific missions that prioritize locations of maximum interest. Because these locations of maximum interest are not known a priori but are rather identified based on in-situ measurements, online adaptation is essential for mission planning. Furthermore, the reliance on a limited-power renewable resource requires an adaptation strategy that maximizes information gathering subject to mobility restrictions imposed by the renewable resource. Our approach addresses these challenges through a clarity-driven ergodic search, where clarity represents a mathematical quantity that has been rigorously linked to differential (information) entropy. In our approach, a target clarity map is adapted online to reflect the prioritization of certain areas based on in-situ measurements, and an ergodic path planner continually re-plans based on the target clarity map and ASV speed limitations (driven by the renewable propulsion source). Focusing on a solar-powered ASV, we present simulations and experiments conducted at Jordan Lake, North Carolina, demonstrating the effectiveness of the proposed approach.

I. INTRODUCTION

Adaptive scientific missions must gather useful information under limited energy while accounting for changing information fields, battery state, and in-situ measurements. This work extends clarity-driven ergodic planning with online target adaptation and energy-informed speed control, then validates the framework in simulation and at Jordan Lake.

I. INTRODUCTION

  • A unified adaptive mission planner must account for information that grows with observation and decays when locations go unvisited, evolving battery state, and real-time in-situ measurements.The motivating objective is to maximize useful scientific information under limited energy.Source: §I · p. 1
  • Existing approaches often simplify energy constraints and assume non-decaying information, limiting sustained tracking of dynamic resources; the proposed framework adapts target clarity online and controls speed for energy constraints.Clarity models time-varying certainty decay, while the planner re-prioritizes informative regions from in-situ measurements.Source: §I · p. 2
  • The framework uses an STGPKF to generate actual and target clarity maps from online measurements, which jointly shape the ergodic objective and prioritize scientifically meaningful regions.The work extends with online adaptation, energy-informed speed control, and experimental validation.Source: §I · p. 2
  • The study evaluates a solar-powered SeaTrac SP-48 ASV on a Jordan Lake wind-characterization mission through simulation and field trials.The scientific objective is to characterize the evolving wind resource.Source: §I · p. 2

A. Energy Dynamics

  • The energy model relates ASV speed to battery state of charge: SOC decreases above break-even speed and increases below it as solar input offsets power use.The model accounts for solar power input, hotel load, and motor power consumption; its constraints bound SOC and speed.Source: A. Energy Dynamics · p. 3
  • Simulation solar input is estimated with a time-varying irradiance model whose period is generally 24 hours and whose average and oscillation amplitude depend on latitude and season.A 24-hour sample of the modeled irradiance is shown in Fig. 2.Source: A. Energy Dynamics · p. 3

B. Information (Clarity) Model

The paper models clarity as an information-theoretic measure linked to differential entropy and evolves it over time using estimates from a spatiotemporal Gaussian Process Kalman Filter. The resulting model accounts for both measurement-driven information gain and natural certainty decay.

B. Information (Clarity) Model

  • The STGPKF estimates spatiotemporal prediction means and variances efficiently by using the equivalence between Gaussian processes and stochastic differential equations.The framework relies on a GP model; for wind speeds, the paper says the non-Gaussian variable can be transformed before applying the model.Source: B. Information (Clarity) Model · pp. 3–4
  • The STGPKF state-space model represents a latent wind field and uses state transition, process-noise, observation, and measurement-noise terms to update estimates across locations.The Kalman filter updates the wind-field estimates as new measurements arrive.Source: B. Information (Clarity) Model · p. 4
  • Clarity q(p, t) ranges from 0 to 1, with higher values indicating lower uncertainty, and is related to differential entropy.The paper characterizes clarity as a function of position and time with a first-order differential equation at each spatial location.Source: B. Information (Clarity) Model · pp. 3–4
  • Clarity evolves through measurement-driven information gain and natural decay as environmental change increases uncertainty over time.For a GP scientific quantity, clarity can be expressed using its prediction variance.Source: B. Information (Clarity) Model · p. 4

C. Wind Speed Transformation

The wind-speed transformation adapts the STGPKF’s zero-mean Gaussian assumption to wind data by modeling measured speeds with a Weibull distribution and mapping them to Gaussian coordinates.

C. Wind Speed Transformation

  • The method addresses the mismatch between wind speed, which is not zero-mean Gaussian, and the STGPKF’s zero-mean Gaussian assumption.The transformation uses the Weibull CDF and inverse Gaussian CDF.Source: C. Wind Speed Transformation · p. 4
  • Wind speed is assumed Weibull-distributed,, with shape k = 2.30 fixed from historical Jordan Lake data and forecasted sustained wind treated as the modal speed for calibration.The resulting scale parameter λ is used to transform wind-speed data before STGPKF input.Source: C. Wind Speed Transformation · p. 4
  • The Gaussian transformation uses µ = 0 and σ = 1 to map the wind-speed data into a zero-mean Gaussian distribution.The transformed value is then supplied to the STGPKF.Source: C. Wind Speed Transformation · p. 4

III. ADAPTIVE MISSION PLANNING METHODOLOGY

The methodology plans a solar-powered ASV to sample wind near a desired rated value while respecting energetic and operational constraints. Its speed controller enforces SOC limits while path planning targets informative regions.

A. Problem Statement

  • The mission allocates sensing toward regions where wind speed is close to a desired rated value, subject to energetic and operational constraints.The mission domain is a two-dimensional region explored by a solar-powered ASV.Source: A. Problem Statement · pp. 4–5

B. Speed Controller

  • Tightened SOC bounds are computed from energy deficit and surplus to prevent future constraint violations that pointwise SOC checks cannot guarantee.Indirect optimal control yields maximum-distance speed that switches at the bounds and remains constant between them, but does not itself provide that constant’s value.Source: B. Speed Controller · p. 5
  • For short missions, speed can be set as a fixed open-loop value targeting terminal SOC or as a time-varying SOC profile tracked by a PID controller.The second approach derives a desired SOC profile bdes(t) and adjusts speed for solar irradiance that differs from the forecast, robustly satisfying a terminal SOC target.Source: B. Speed Controller · p. 5
  • For long-duration missions, constant speed generally drives SOC to its upper or lower limits, so speed variation is required; persistent-endurance optimization is outside this work’s scope.The paper notes a separate learning-based approach for updating speed at the end of each day [35].Source: B. Speed Controller · p. 5

C. Clarity-Driven Path Planning

Clarity-driven planning minimizes the gap between targeted and actual clarity through a filter, target-distribution generator, and path planner. The framework diagram identifies clarity-driven path planning as one component of the integrated control system.

C. Clarity-Driven Path Planning

  • The clarity-driven planning process comprises the STGPKF, target clarity distribution generator, and path planner.The planner seeks to minimize the domain-averaged gap between targeted and actual clarity.Source: C. Clarity-Driven Path Planning · p. 5
  • In the integrated control framework, blue blocks denote clarity-driven path planning.Fig. 3 is a block diagram of the proposed framework.Source: Figure 3 · p. 6
  • Fig. 4 presents an example of tightened state-of-charge constraints calculated over a 24-hour period.Source: Figure 4 · p. 6

1) Spatiotemporal Gaussian Process Filter (STGPKF):

The planning pipeline updates a spatiotemporal clarity estimate, converts target clarity into a spatial distribution, and uses ergodic control to steer the ASV toward that target while maintaining domain coverage.

1) Spatiotemporal Gaussian Process Filter (STGPKF):

  • The STGPKF combines spatial correlations from a Gaussian-process prior with recursive Kalman filtering to update a time-evolving clarity map from sequential observations.The filter propagates the clarity state and updates it when new observations arrive.Source: 1) Spatiotemporal Gaussian Process… · p. 6

2) Target Clarity Generation:

  • The target clarity map is derived from STGPKF wind estimates, with target decay governed by distance from rated wind speed and rated clarity set at that speed.The resulting map specifies the clarity level sought across the domain.Source: 2) Target Clarity Generation · p. 6

3) Clarity-Driven Path Planner:

  • Ergodic control matches trajectory occupancy to the target distribution using Fourier statistics, while its Sobolev metric prioritizes global coverage before fine local variations.The planner computes velocity commands along the negative spatial gradient of the ergodic cost, using desired speed from the energy controller.Source: 3) Clarity-Driven Path Planner · pp. 6–7
  • The planner normalizes local clarity deficits into a spatial probability density, assigning higher relative dwell-time weight where actual clarity lags the target.The density serves as the target spatial distribution for ergodic trajectory optimization.Source: 3) Clarity-Driven Path Planner · p. 6

D. Boundary Avoidance

Boundary avoidance blends the nominal velocity with an inward correction as the ASV approaches the mission-domain boundary, then sends corrected speed and heading commands to the low-level controllers.

D. Boundary Avoidance

  • As the ASV nears the boundary, the correction rotates its velocity toward the domain interior while preserving speed magnitude and maintaining the minimum standoff distance.When distance to the boundary is at least dmin, the commanded velocity equals the nominal velocity.Source: D. Boundary Avoidance · p. 7
  • The corrected velocity is converted to speed and heading commands for the ASV’s low-level controllers.Source: D. Boundary Avoidance · p. 7

IV. SIMULATION STUDY

The simulation study examines how target adaptation and low-level planning affect sampling, field reconstruction, and clarity deficit, using diagnostic environments and a Monte Carlo study.

IV. SIMULATION STUDY

  • The study isolates target-adaptation and planner effects in two diagnostic environments, then tests sensitivity to wind-field correlation scales through Monte Carlo trials.Source: §IV · p. 7
  • Table II lists the strategies used in the simulation study.Source: Table II · p. 8
  • The simulations use the Jordan Lake mission domain shown in Fig. 5.Source: Figure 5 · p. 8

A. Ablation and Sensitivity Study Design

The study compares adaptive and nonadaptive strategies across static and time-varying wind environments, evaluating target sampling, reconstruction, and clarity matching. Target selectivity can improve target-directed sampling, but aggressive settings can compromise exploration and other metrics.

1) Compared Strategies:

  • The seven strategies vary planner and target source: adaptive strategies update targets from STGPKF estimates, while ground-truth-target strategies use targets computed from simulated wind.Nonadaptive strategies use an initially uniform target; BB-IPP and the ergodic controller are compared as low-level planners.Source: 1) Compared Strategies · p. 8, A. Ablation and Sensitivity Study Design · p. 8

2) Simulation Environments:

  • The half-domain environment contrasts near-rated and strongly off-target wind, while moving-pocket conditions test whether controllers revisit multiple relevant regions as they change over time.The diagnostic environments are shown in Fig. 6.Source: 2) Simulation Environments · p. 8, Figure 6 · p. 8

3) Evaluation Metrics and Parameters:

  • Evaluation measures target-neighborhood sampling, wind-field RMSE, and ground-truth-target clarity deficit; lower RMSE and deficit are better.The metrics distinguish sampling concentration, global estimation accuracy, and trajectory alignment with the target distribution.Source: 3) Evaluation Metrics and Parameters · p. 8

B. Target-Adaptation Sensitivity

  • Across the sensitivity tests, increasing λcd generally raises near-rated sampling, but aggressive selectivity can reduce broad exploration and degrade other metrics.At λcd = 0, adaptive and nonadaptive controllers are identical; in the moving-pocket case, the in-target fraction rises to 79.5% at λcd = 0.1 before falling to 32.4% at λcd = 0.25.Source: B. Target-Adaptation Sensitivity · pp. 8–9, Figure 7 · p. 9
  • In the half-domain case, λcd = 0.01 raises the ergodic controller’s in-target fraction from 46.7% to 85.1%, while RMSE falls from 1.67 to 1.62 and clarity deficit from 0.086 to 0.077.This moderate-selectivity result is reported for a large, static relevant region.Source: B. Target-Adaptation Sensitivity · p. 8
  • Estimated-target clarity deficit can understate poorly explored regions because the estimated wind field may assign them low importance, so primary comparisons use ground-truth-target deficit.Source: B. Target-Adaptation Sensitivity · p. 9

C. Diagnostic Planner Comparisons

Adaptation consistently shifts measurements toward target wind conditions, but target concentration and whole-field reconstruction can trade off. Outcomes also depend on whether relevant regions are static or moving and on the planner’s ability to distribute sensing effort.

1) Half-Domain Environment:

  • Restricting the half-domain transect raises in-target measurements from 43.2% to 95.7% and lowers clarity deficit from 0.093 to 0.077; adaptation raises in-target fractions for both planners.The ground-truth-target ergodic strategy has the lowest deficit, 0.072, while the full-domain transect has the lowest RMSE, 1.55.Source: Figure 8 · p. 9, 1) Half-Domain Environment · p. 9

D. Monte Carlo Sensitivity Study

  • Across 36 settings, adaptation raises in-target sampling by 15.50 percentage points for the ergodic controller and 14.85 points for BB-IPP, while mean RMSE changes are +3.44% and +3.77%, respectively.Source: D. Monte Carlo Sensitivity Study · pp. 9–10

2) Moving-Pocket Environment:

  • In moving pockets, adaptation raises in-target fractions to 34.7% for BB-IPP and 32.4% for ergodic control; ground-truth-target ergodic control reaches 44.2% and the lowest deficit, 0.0068.The trajectories indicate that BB-IPP may stay with a pocket after it moves, whereas ergodic control continues to visit multiple pockets.Source: 2) Moving-Pocket Environment · p. 9, Figure 9 · p. 10

D. Monte Carlo Sensitivity Study

  • Ground-truth targets reduce clarity deficit by averages of 8.61% for ergodic control and 7.81% for BB-IPP, alongside RMSE increases of 5.76% and 5.22%, respectively.The study also reports increased clarity deficit for adaptive ergodic control in 35 of 36 settings.Source: D. Monte Carlo Sensitivity Study · p. 10

E. Discussion

The discussion distinguishes target-directed sampling from full-field reconstruction and clarity-deficit reduction, while noting that estimated targets can misrepresent insufficiently observed regions. Field missions test targeted wind sampling and SOC-based speed control, but do not establish persistent energy balance.

E. Discussion

  • Online adaptation directs measurements toward desired wind conditions, but target sampling, whole-field reconstruction, and clarity deficit remain distinct objectives; ergodic planning preserves broader target coverage than BB-IPP.The STGPKF-derived target can underestimate insufficiently observed regions, producing mismatches with the ground-truth target map.Source: E. Discussion · p. 10

V. EXPERIMENTAL RESULTS

  • The field evaluation compares constant-speed 90-minute missions, 90-minute missions with closed-loop SOC control, and 3-hour missions with SOC control.The constant-speed comparison isolates targeted sampling; the latter missions examine planning alongside energy-aware speed control.Source: §V · p. 10

A. Setup

  • The SeaTrac SP-48 ASV was tested at Jordan Lake with an ultrasonic wind sensor, GPS, and real-time SOC measurements.The experimental domain matched the simulation domain.Source: A. Setup · p. 10

C. 90 Minute Missions With Closed-Loop SOC Control

B. 90 Minute Missions Without Closed-Loop SOC Control

C. 90 Minute Missions With Closed-Loop SOC Control

D. 3 Hour Missions

The 3-hour field missions show targeted wind sampling during SOC-controlled operation, while the broader conclusions distinguish targeted sampling from reconstruction and coverage. The authors note that estimated-mean targets can undervalue unvisited regions, and field comparisons do not establish global reconstruction or complete coverage.

D. 3 Hour Missions

  • In 3-hour missions with closed-loop SOC control enabled, the ergodic trajectory prioritized the northern domain, where measured winds were closer to rated speed, and its histogram concentrated more near zero than the transect run.Source: D. 3 Hour Missions · p. 13

E. Summary of Results

  • The experiments show targeted sampling and SOC-based speed adjustment operating together on the physical ASV.The measured-minus-rated deviations indicate proximity to the scientific target, not error against an independently measured ground-truth field.Source: E. Summary of Results · p. 13

VI. CONCLUSIONS AND FUTURE WORK

  • The framework combines clarity for evolving information, an in-situ-updated target clarity map, ergodic planning, and SOC-based speed control.Simulations and Jordan Lake field experiments demonstrate that the components operate together and direct sensing toward scientifically relevant conditions.Source: §VI · p. 13
  • Online adaptation increases sampling near rated wind speed, but targeted sampling, spatial clarity, and full-field reconstruction are distinct objectives whose balance depends on selectivity, planner, and environment.Mild selectivity can improve all three metrics when the interesting region is spatially coherent; stronger selectivity or moving regions can trade reconstruction and coverage for relevant measurements.Source: §VI · p. 13
  • Because target generation depends on estimated mean, it may assign little value to unvisited regions mistakenly estimated as uninteresting.Future work will consider additional running statistics, spatially varying kernel parameters, and direct coupling of energy and information objectives in online optimization.Source: §VI · pp. 13–14
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