Multi-Agent Deferred-Decision Trajectory Optimization with Anytime-Valid Target Retention for Moving Candidates

Farbod Siahkali; Mengxue Hou; Vijay Gupta

eess.SYOct 12, 2026

Multi-Agent Deferred-Decision Trajectory Optimization with Anytime-Valid Target Retention for Moving Candidates

Authors: Farbod Siahkali, Mengxue Hou, Vijay Gupta

Organizations: Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA · Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

Abstract

We study multi-agent terminal interception when one of several moving candidates is the unknown target and both target identity and candidate terminal locations are uncertain. We develop a receding-horizon deferred-decision trajectory optimization (DDTO) controller that combines conformal terminal-location prediction, sequential candidate rejection, capacity-constrained assignment, and candidate-contingent planning. Under exchangeability conditions for terminal and identity residuals, with predictable querying, we establish fixed-time terminal-location coverage and anytime-valid target retention. At the final replan, when one control step remains, we bound the joint probability that a tightened-set DDTO plan passes nonlinear rollout verification but capture fails. The closed-loop controller applies fallback guidance to any agent without a verified DDTO plan and, across 100 paired scenarios, captures 79% of targets under the strict control-effort budget and 85% when that budget is relaxed.

Figures & tables

Fig. 1: Closed-loop HoloOcean demonstration of multi-AUV terminal interception at replan $k=12$ . (a) HoloOcean state after executing the control applied at the preceding replan. (b) Corresponding planner state, initialized from simulator feedback, showing assignments, predicted terminal centers, conformal terminal regions, common DDTO prefixes, and candidate-contingent branches. (c) HoveringAUV model used for the agents. The target is highlighted in the figure but is not available to the controller.

Fig. 2: Statistical component validation over 1000 Monte Carlo trials. Terminal coverage, prediction error and conformal radius, and mean non-target rejection are reported. Shading gives pointwise 95% intervals.

Method	Capture (%) $\uparrow$	Team effort ( $10^{3}$ N 2 s) $\downarrow$
Proposed DDTO	79.0%	214.9 [164.1, 274.5]
CMPC [ 9 ]	67.0%	233.4 [168.6, 281.8]
DDMP [ 10 ]	46.0%	257.3 [187.4, 300.0]
Fallback-only	6.0%	300.0 [300.0, 300.0]
Fallback-disabled	13.0%	46.6 [34.4, 65.6]
Center–commit	13.0%	217.2 [171.9, 300.0]

TABLE I: Closed-loop comparison at

B_{a}=150\times 10^{3}

N 2 s over 100 paired scenarios. Effort is reported as median [IQR]. Bold denotes the highest observed capture rate.

Variant	Candidate rejection	Query rule	Assignment	Capture $\uparrow$	Effort ( $10^{3}$ N 2 s) $\downarrow$	Complete verified-plan rate (%) $\uparrow$
Proposed DDTO	Yes	Balanced evidence	Reach cost	79.0%	214.9 [164.1, 274.5]	80.0 [80.0, 85.0]
No candidate rejection	No	Balanced evidence	Reach cost	68.0%	268.1 [234.1, 300.0]	80.0 [75.0, 80.0]
Uniform-random query	Yes	Uniform random	Reach cost	67.0%	172.7 [121.3, 229.6]	85.0 [80.0, 86.0]
Clustered assignment	Yes	Balanced evidence	Terminal clustering	63.0%	260.5 [209.2, 300.0]	80.0 [80.0, 85.0]

TABLE II: Component ablations at

B_{a}=150\times 10^{3}

N 2 s over 100 paired scenarios. Effort and complete verified-plan rate are reported as median [IQR]. Bold denotes the highest observed capture rate.

Fig. 3: Planning diagnostics under the relaxed

250\times 10^{3}

N 2 s per-agent budget over 100 paired scenarios: (a) post-query retained-set size and (b) complete verified-plan rate for the compared controllers. Shading denotes pointwise 95% intervals.

Method	Capture (%) $\uparrow$	Team effort ( $10^{3}$ N 2 s) $\downarrow$
Proposed DDTO	85.0%	271.3 [181.4, 339.3]
CMPC [ 9 ]	74.0%	253.2 [162.4, 357.4]
DDMP [ 10 ]	74.0%	334.7 [246.4, 428.1]
Fallback-only	28.0%	500.0 [477.5, 500.0]
Fallback-disabled	14.0%	46.8 [34.9, 67.0]
Center–commit	12.0%	288.2 [208.2, 380.6]

TABLE III: Closed-loop comparison after relaxing the per-agent effort budget to

B_{a}=250\times 10^{3}

N 2 s over the same 100 paired scenarios. Effort is reported as median [IQR]. Bold denotes the highest observed capture rate.

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Jun 21, 2026J/K move · Enter open · S save

Active Sensing and Deferred-Decision Trajectory Optimization for Robust Target Identification

Farbod Siahkali, Mengxue Hou, Vijay Gupta

Department of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47906, USA · Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA

Constrained Motion Planning Trajectory Optimization Trajectory Generation Informative Path Planning Active Sensing Constrained Optimization+1

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We study trajectory optimization in mobile sensing systems that must identify which member of a finite candidate set is the true target, while maintaining reachability to all potential candidate targets, under resource constraints. Deferred-Decision Trajectory Optimization (DDTO) addresses this setting by computing trajectories that reach individual targets but remain coincident for as long as possible before separating toward different targets. We propose Active-Sensing DDTO (AS-DDTO), which extends DDTO by adding a trajectory-dependent information-acquisition term to the planning objective. The resulting planner maintains reachability to candidate targets while biasing the coincident portion of the trajectories toward regions that enable earlier target identification. The framework supports Bayesian updates and conformal candidate-set updates for distance-dependent sensing. We derive a mixed-integer conic reformulation and provide guarantees on recursive feasibility, belief concentration, and fixed-time coverage for the raw conformal candidate set. Numerical simulations show improved target identification compared with standard DDTO under distance-dependent sensing uncertainty and limited sensing budget.

Abstract

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