Homotopic information gain for sparse active target tracking

Jennifer Wakulicz; Ki Myung Brian Lee; Teresa Vidal-Calleja; Robert Fitch

cs.ROFeb 20, 2026

Homotopic information gain for sparse active target tracking

Authors: Jennifer Wakulicz, Ki Myung Brian Lee, Teresa Vidal-Calleja, Robert Fitch

Organizations: Australian Centre for Robotics, School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Camperdown, 2006, NSW, Australia · Department of Electrical and Computer Engineering, UC San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA · School of Mechanical and Mechatronics Engineering, University of Technology Sydney, Ultimo, 2007, NSW, Australia

Abstract

The problem of planning sensing trajectories for a mobile robot to collect observations of a target and predict its future trajectory is known as active target tracking. Enabled by probabilistic motion models, one may solve this problem by exploring the belief space of all trajectory predictions given future sensing actions to maximise information gain. However, for multi-modal motion models the notion of information gain is often ill-defined. This paper proposes a planning approach designed around maximising information regarding the target's homotopy class, or high-level motion. We introduce homotopic information gain, a measure of the expected high-level trajectory information given by a measurement. We show that homotopic information gain is a lower bound for metric or low-level information gain, and is as sparsely distributed in the environment as obstacles are. Planning sensing trajectories to maximise homotopic information results in highly accurate trajectory estimates with fewer measurements than a metric information approach, as supported by our empirical evaluation on real and simulated pedestrian data.

Figures & tables

Panel of Figure 1 — Fig. 1 : Heatmaps showing visitation frequency at sensing locations for the active target tracking problem on the ATC dataset. A conventional tracking approach (left) is compared to the sparse homotopic approach proposed in this paper (right). With our proposed approach, the sensing robot is only concerned with how a target manoeuvres around obstacles, reducing planning and sensing resources while still producing accurate estimates of the target trajectory.

Panel of Figure 2 — Fig. 2 : Illustrations of homotopy classes and $h$ -signature calculation. [ 9 ]

Panel of Figure 3 — Fig. 3 : Heatcubes of homotopic information gain at different sensing locations and times ( $z$ -axis). Red line shows the test trajectory travelling upwards in time.

Panel of Figure 4 — Fig. 4 : Left: one of the environments used to simulate pedestrian trajectories, here with three obstacles. Middle: The real pedestrian ATC mall dataset with five obstacles present. Right: the THÖR dataset with both real and augmented pedestrian trajectories with three obstacles present.

	Dataset
	Simulated					THÖR	ATC
$O$	3	4	5	6	7	3	5
$H$	4	6	7	11	12	6	13

TABLE I : The number of obstacles

O

and homotopy classes

H

present in each dataset used for evaluation.

Panel of Figure 6 — Fig. 5 : Results for active target tracking on the simulated pedestrian dataset with three obstacles.

Panel of Figure 7 — Fig. 6 : Results for active target tracking on the simulated pedestrian datasets increasing number of obstacles.

Panel of Figure 8 — Fig. 7 : Results for active target tracking on the ATC mall pedestrian dataset with five obstacles.

Panel of Figure 9 — Fig. 8 : Results for active target tracking on the augmented THÖR pedestrian dataset with three obstacles.

Fig. 9 : Total tracking experiment length for the real datasets.

Panel of Figure 11 — Fig. 10 : Snapshots of predictions output by a homotopic GMM during an active target tracking experiment using homotopic information gain 10(a) - 10(e) and metric information gain 10(f) - 10(j) . Black solid path is the elapsed ground truth test trajectory at the given time. Dotted path indicates future ground truth trajectory remaining. Coloured crosses denote all measurements taken by the sensing robot up to time $t$ , where colours serve to differentiate between approaches (orange for the metric approach, blue for the homotopic approach). Shaded regions show the variance of the mean shown in solid colour, where colours differentiate GMM components. Transparency is proportional to component weight.

Fig. 11 : Distributions of displacement errors averaged over the full trajectory length for each dataset with (labelled with $\varnothing$ ) and without the empty $h$ -signature.

Fig. 12 : Distributions of the number of measurements taken per tracking experiment for each dataset with (labelled with $\varnothing$ ) and without the empty $h$ -signature.

Datasets without $h=()$
	Sim-3	Sim-4	Sim-5	Sim-6	Sim-7	ATC	THÖR
Ours	100	100	100	99	91	81	100
Metric	100	100	100	99	98	95	100
Datasets with $h=()$
	Sim-3 $\varnothing$	Sim-4 $\varnothing$	Sim-5 $\varnothing$	Sim-6 $\varnothing$	Sim-7 $\varnothing$	ATC $\varnothing$	THÖR $\varnothing$
Ours	96.67	100	98.9	90	91	85	81

TABLE II : Success rates (%) for our homotopic approach versus the metric approach before and after the empty

h

-signature is introduced.

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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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