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Learning Direct Control from Optimization for Dynamic Target Tracking

Bing Sun, Yue Lin, Canhui Wen, Xin Chen, Yang Liu, Dong Wang, Huchuan Lu

arXiv:2610.34929v1cs.RO

TL;DR

Dynamic target tracking must balance visibility, obstacle clearance, and smooth feasible motion as targets and environments change. LECO learns direct control from trajectory objectives through differentiable kinematic rollout, with expert guidance and a predictive safety fallback. Across simulated obstacle densities it reports the best tracking success and lowest root-mean-square linear jerk among evaluated methods, alongside real-world tracking demonstrations.

  • Problem

    Dynamic tracking requires robots to maintain target visibility while navigating obstacles with smooth, feasible controls as the target and local environment change.

    Source: §I · p. 1

  • Method

    LECO trains a direct-control policy by rolling predicted control sequences through a differentiable kinematic model, using task objectives, decaying expert guidance, and a predictive safety lock with classical fallback.

    Source: §I · pp. 1–2

  • Results

    Across three simulated obstacle densities, LECO achieves the lowest root-mean-square linear jerk and highest tracking success among evaluated methods, with 4.25–5.63 ms per-cycle computation.

    Source: §I · p. 2

  • Takeaways & Limitations

    Real-world experiments demonstrate tracking through indoor narrow passages and outdoor forest environments, while simulations report improved smoothness and tracking robustness.

    Source: §I · p. 2, §VI · p. 8

Abstract

from arXiv · show

Dynamic target tracking requires a mobile robot to maintain target visibility while navigating obstacles with smooth, feasible controls. Online trajectory optimization explicitly encodes these objectives but requires repeated numerical solving, whereas waypoint-based neural policies separate geometric prediction from control execution. We introduce LECO, a framework that transfers tracking optimization into offline learning of a direct-control policy. LECO predicts control sequences and maps them to trajectories through a differentiable kinematic model, allowing trajectory-level objectives to directly guide control learning. A decaying expert-guidance curriculum initializes effective tracking behavior and progressively shifts learning toward these task objectives. At deployment, a predictive safety lock checks short-horizon obstacle clearance and invokes a classical planning and control fallback when the predicted motion is unsafe or the target prediction is invalid. Across three simulated obstacle densities, LECO reduces root-mean-square linear jerk by 14.1--31.2\% relative to the best competing method for this metric and achieves the highest tracking success rate, with per-cycle computation times of 4.25--5.63\,ms. Experiments on two robot platforms further demonstrate tracking through indoor narrow passages and outdoor forest environments. These results demonstrate that learning direct control from optimization enables smooth and robust dynamic target tracking.

I. INTRODUCTION

Dynamic target tracking must balance target visibility, obstacle clearance, and smooth feasible motion as the target and environment change. LECO transfers trajectory-level objectives into direct-control learning through a differentiable kinematic rollout.

I. INTRODUCTION

  • LECO directly predicts controls and propagates trajectory-level tracking objectives through a differentiable kinematic rollout to train the policy.This connects visibility, obstacle clearance, and smoothness objectives to the motion produced by executable controls.Source: §I · pp. 1–2
  • A decaying expert-guidance curriculum initializes effective tracking behavior, then progressively shifts learning toward task objectives.The policy predicts a control sequence and evaluates desired target distance, clear lines of sight, obstacle clearance, and smooth motion along its rollout.Source: §I · pp. 1–2
  • A predictive safety lock checks short-horizon obstacle clearance and invokes a classical A* and MPC branch when motion is unsafe or target prediction is invalid.Neural execution resumes when target prediction and clearance checks permit it and the lock duration has elapsed.Source: §I · pp. 1–2
  • Across three simulated obstacle densities, LECO achieves the lowest root-mean-square linear jerk and highest tracking success, with 4.25–5.63 ms per-cycle computation.Real-world experiments also demonstrate tracking through indoor narrow passages and outdoor forest environments.Source: §I · p. 2
  • Platform-specific policies demonstrate real-world tracking with a Unitree G1D indoors and an AgileX HUNTER 2.0 in a forest.Figure 1 depicts the narrow-passage and forest settings, with first-person views showing estimated target distance.Source: Figure 1 · p. 1, §I · p. 2

II. RELATED WORK

The related work contrasts repeated online trajectory optimization with learned planning and control, then motivates LECO’s offline direct-control policy and safety fallback.

A. Classical Optimization-Based Target Tracking

  • In narrow passages and tight corners, online SQP and L-BFGS solvers can reach local minima or zero-velocity deadlocks; solver burden grows with complexity, and long-horizon errors can accumulate.Traditional methods encode line-of-sight maintenance and obstacle clearance as cost terms.Source: A. Classical Optimization-Based Target… · p. 2

B. Learning-Based Motion Planning and Control

  • Waypoint- and trajectory-based policies separate geometric prediction from platform control, which can create a mismatch between training objectives and executable controls.LECO instead predicts control sequences and uses explicit target-tracking and line-of-sight objectives.Source: B. Learning-Based Motion Planning and… · p. 2

C. Optimization Distillation and Safe Deployment

  • Optimization-distillation methods often target generic planning or point-to-point navigation; direct cost optimization can produce near-zero controls early, while black-box policies lack deterministic OOD safety guarantees.CBF filters add online constrained filtering, while fallback strategies can disrupt dynamic-tracking continuity.Source: C. Optimization Distillation and Safe… · p. 3

A. Framework Overview

  • Traditional platform-specific solvers generate feasible control sequences online using search or optimization, whereas LECO replaces this with offline policy learning and differentiable trajectory rollout.The traditional solver uses a predicted target trajectory, environment representation, and platform-specific motion and safety parameters.Source: A. Framework Overview · p. 3
  • LECO trains on local geometry, robot motion, target-relative state, and line-of-sight features, then executes one receding-horizon action unless a safety check triggers hybrid A* and MPC.The fallback is invoked when target prediction becomes invalid or predicted motion becomes unsafe.Source: A. Framework Overview · p. 3

B. Kinematic-Integrated Control Policy

LECO estimates target motion, predicts future controls directly from robot-centered observations, and rolls those controls through differentiable platform kinematics. This connects trajectory-level tracking objectives to the controls the robot executes.

B. Kinematic-Integrated Control Policy

  • A degree-2m Bézier trajectory estimates target motion from the latest m + 1 observed positions, with historical positions constraining the fit and minimum acceleration determining remaining degrees of freedom.The trajectory is parameterized over T = mτ; ξ = 0 marks its latest update.Source: B. Kinematic-Integrated Control Policy · p. 3
  • The predicted target state is represented in the robot-relative frame by target distance, relative bearing, and target velocity direction.The angular encoding uses [sin ϕ, cos ϕ].Source: B. Kinematic-Integrated Control Policy · p. 3
  • LECO predicts future control sequences directly from observations rather than first predicting geometric waypoints.The policy executes only the first predicted control in a receding-horizon manner.Source: B. Kinematic-Integrated Control Policy · p. 3
  • The policy uses an 80 × 80 robot-centered local ESDF, current velocities, a 6-D target-relative state, and eight LoS ESDF samples to predict 30 controls over a 3.0 s horizon.The policy runs at 10 Hz and executes the first predicted control.Source: B. Kinematic-Integrated Control Policy · p. 3
  • Differentiable platform-specific rollouts let spatial objectives, including target tracking and line-of-sight constraints, backpropagate to the control policy.The rollout uses the corresponding differential-drive or Ackermann kinematic model.Source: B. Kinematic-Integrated Control Policy · p. 4

C. Cost-Guided Optimization-to-Policy Learning

LECO trains direct-control predictions with differentiable task costs propagated through a kinematic rollout, while constraining planar motion and control inputs.

C. Cost-Guided Optimization-to-Policy Learning

1) Traditional Costs as Differentiable Losses:

The loss combines collision, control-feasibility, and smoothness terms with target-visibility and low-clearance escape objectives. Visibility uses target prediction and sampled line-of-sight clearance, while an ESDF-based guidance term encourages motion toward greater clearance.

1) Traditional Costs as Differentiable Losses:

2) Curriculum Expert-to-Cost Knowledge Transfer:

A decaying expert-guidance curriculum addresses early near-zero controls by shifting training from expert anchoring toward physics- and geometry-driven cost optimization.

2) Curriculum Expert-to-Cost Knowledge Transfer:

D. Predictive Safety Lock for Hybrid Deployment

The predictive safety lock checks the predicted motion before execution and switches to a classical branch when the neural trajectory is unsafe or the target prediction is invalid. Neural control resumes only after the lock expires and the target and safety checks pass.

D. Predictive Safety Lock for Hybrid Deployment

  • The safety lock switches from neural control to hybrid A* and MPC when a short-horizon check finds unsafe predicted motion or an invalid target prediction.The classical branch supplies an interim safe tracking path or a reacquisition path based on the latest valid target state.Source: D. Predictive Safety Lock for Hybrid… · p. 5
  • The safety horizon checks the first M predicted control steps; with M = 10, it spans 1.0 s.The rollout uses the platform kinematic model at each control cycle.Source: D. Predictive Safety Lock for Hybrid… · p. 5
  • Neural control resumes only when the target prediction is valid, the lock has expired, and the short-horizon safety check passes.The classical branch remains active for at least Nlock = 6 control cycles, or 0.6 s at 10 Hz.Source: D. Predictive Safety Lock for Hybrid… · p. 5

A. Experimental Setup

The evaluation compares LECO with three tracking or planning baselines on shared maps, target trajectories, initial states, and control frequency. It measures tracking smoothness, visibility, runtime, and success across obstacle densities.

A. Experimental Setup

  • LECO is compared with Elastic-Tracker, YOPO-Planner, and A*+MPC; an ablation removes the safety lock and stops when clearance falls below its threshold.YOPO uses the same tracking reference point as its planning goal without explicit target-visibility objectives, while A*+MPC also serves as LECO’s early-stage expert.Source: A. Experimental Setup · p. 5
  • Fig. 5 contrasts target-loss events for Elastic-Tracker and YOPO with LECO tracking and shows dense-obstacle trajectories in Maze-200 and Maze-50 with temporary disturbances.The caption reports one loss event for Elastic-Tracker, three for YOPO, and no loss for LECO.Source: Figure 5 · p. 6
  • The simulated 80 m × 80 m map uses 50, 100, or 150 randomly generated static obstacles.Obstacle length and width are independently sampled from [0.5, 18] m.Source: A. Experimental Setup · p. 6
  • Each obstacle density has 50 independent continuous tracking trials, with all methods using the same maps, target trajectories, initial states, and control frequency.Reported measures include linear jerk RMS, occlusion rate, per-cycle computation time, and tracking success; success excludes target-loss events lasting longer than 4 s.Source: A. Experimental Setup · p. 6

B. Comparative Evaluation

LECO achieves the lowest linear jerk across the evaluated obstacle densities and improves tracking success and occlusion relative to its safety-lock ablation. Challenging-scenario evaluations and real-world trials further examine tracking in dense layouts, disturbances, narrow passages, and outdoor settings.

B. Comparative Evaluation

  • LECO reduces Ev by 33.2%, 40.9%, and 47.6% over the best external baseline across obstacle densities; at 150 obstacles, occlusion is 6.32% versus 19.72% for the ablation.The full model also maintains 92% and 86% success with 100 and 150 obstacles, respectively.Source: B. Comparative Evaluation · p. 6
  • LECO maintains continuous tracking without target loss in Fig. 5, while Elastic-Tracker has one target-loss event and YOPO has three.LECO’s 4.25–5.63 ms runtime is comparable to optimization-based baselines; it surpasses the A*+MPC expert, while Elastic-Tracker is slightly faster in two settings.Source: B. Comparative Evaluation · p. 6

C. Challenging Scenarios

  • Across Mess-200, Maze-200, and Maze-50 with temporary obstacles, the neural policy supplies 88.57–95.81% of control decisions; Mess-200 has no collisions and four failed trials.Maze-200 retains a 95.81% neural-policy ratio despite narrow passages and consecutive turns; temporary disturbances lower the ratio to 88.57%, and LECO succeeds in 82% of trials and recovers the target in 19 of 28 loss events.Source: C. Challenging Scenarios · p. 6
  • Real-world experiments use a differential-drive Unitree G1D indoors and an Ackermann-steered AgileX HUNTER 2.0 outdoors; indoor trials include an S-shaped passage and temporary obstacle disturbance.Fig. 8 describes continuous tracking through consecutive turns in constrained space and the response of the predictive safety lock to disturbance.Source: Figure 7 · p. 7, Figure 8 · p. 7
  • FoV heatmaps show the target remains within the effective field of view for most of the tracking process.Fig. 6 presents heatmaps for Mess-200, Maze-200, and Maze-50 with temporary obstacles.Source: Figure 6 · p. 6, C. Challenging Scenarios · p. 7

V. REAL-WORLD EXPERIMENTS

Real-world experiments demonstrate tracking across narrow indoor passages, sudden obstacle disturbances, and an unstructured forest. The conclusion reports stable operation across these settings while noting that the framework is limited to planar kinematics and 2-D ESDF constraints.

V. REAL-WORLD EXPERIMENTS

  • Experiments use a differential-drive Unitree G1D indoors and an Ackermann-steered AgileX HUNTER 2.0 outdoors across three challenging scenarios.The scenarios assess stability, obstacle avoidance, observability, and long-horizon operation under different platform dynamics and environments.Source: §V · p. 7
  • In an S-shaped narrow passage, the robot completes long-range tracking through consecutive turns while maintaining stable obstacle avoidance and keeping the target in view for most of the process.The route includes constrained free space and intermittent occlusions.Source: §V · p. 7
  • When a temporary obstacle makes predicted neural motion unsafe, the safety lock triggers classical fallback; control returns to the neural policy after the obstacle is bypassed.The fallback guides the robot around the obstacle while tracking continues without prolonged interruption.Source: §V · p. 7
  • In the forest, the Ackermann platform tracks through irregular natural obstacles and recovers the target after temporary occlusion or loss.The figure depicts continuous tracking and obstacle avoidance through irregularly distributed obstacles.Source: §V · pp. 7–8, Figure 9 · p. 7

VI. CONCLUSION AND FUTURE WORK

  • LECO demonstrates stable real-world operation across narrow passages, sudden disturbances, and unstructured environments, alongside improved simulation tracking success, visibility, and smoothness.The conclusion also reports competitive millisecond-level computation.Source: §VI · p. 8
  • The current framework mainly considers planar kinematics and 2-D ESDF constraints; richer dynamics, 3-D environments, and more complex dynamic interactions are future work.Source: §VI · p. 8
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