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LEAP: Learning Emergent Active Perception for Quadruped Navigation

Ü. Bora Gökbakan, Stéphane Caron, Philippe Souères

arXiv:2609.17628v1cs.ROcs.CV

TL;DR

Goal-oriented navigation over hazardous terrain requires agents to discover goals and route features that are visible only from selected viewpoints, while hand-designed sensing rewards can conflict with task objectives. LEAP learns camera and body control from task reward alone using gaze-invariant belief maps. It achieves 92.7% mean success on unseen layouts, outperforming scripted sweeps and passive perception, and its navigation policies steer separately trained quadruped locomotion policies in simulation.

  • Problem

    In hazardous, non-linear terrain, route features and goals may be visible only from selected viewpoints, while hand-designed curiosity or coverage rewards can conflict with task value.

    Source: §I · p. 1, §III · p. 2

  • Method

    LEAP trains one policy to control body motion and camera orientation from task reward alone, using gaze-invariant belief maps to integrate depth observations.

    Source: §I · p. 1

  • Results

    92.7% mean success on 100 unseen layouts for Active, versus 74.2% for Sweep and 34.5% for Passive, within 4.6 points of the GT oracle.

    Source: §I · p. 1, B. Goal-Reaching on Held-Out Terrain · p. 7

  • Takeaways & Limitations

    LEAP navigation policies can steer separately trained locomotion policies on a full-body quadruped in simulation over held-out terrains.

    Source: §I · p. 1, §VI · p. 8

    The 2.5D belief-map representation cannot capture overhangs.

    Source: §VI · p. 8

Abstract

from arXiv · show

Active perception allows autonomous agents to select their viewpoints rather than passively process the viewpoints given to them, enabling them to target where to reduce uncertainty about their environment. Learned systems typically encourage this behavior with hand-designed proxy objectives, such as coverage or curiosity bonuses, that may conflict with the task. In this work, we propose a method to learn emergent active perception (LEAP) without augmentation of the task objective. We formulate the problem of goal-oriented navigation over hazardous terrains with goals that must be discovered visually. We then propose an architecture for navigation policies with active perception, and train them on a terrain curriculum where task pressure alone leads to the emergence of gaze control. Key to this emergence, LEAP works on a gaze-invariant representation that integrates depth images into egocentric belief maps. We validate its performance in held-out evaluation scenarios, where it achieves a 92.7% success rate, compared to 74.2% for scripted or 34.5% for passive perception, and comes within 4.6 points of a privileged oracle. We validate that LEAP navigation policies, unchanged, can be directly applied to steering quadrupedal locomotion policies in physics simulation.

I. INTRODUCTION

LEAP treats viewpoint selection as part of goal-directed control: one policy commands the body and camera, with gaze learned from task reward rather than a separate sensing objective. Its gaze-invariant belief maps support active sensing, and the method achieves strong held-out navigation results.

A. Active Perception

  • In hazardous, non-linear terrain, route features may lie below, beside, or behind a robot, so a limited-field-of-view sensor must be actively aimed.Prior forward-facing locomotion cameras suffice when upcoming decisions enter the view successively,.Source: §I · p. 1, A. Active Perception · p. 1
  • Hand-designed curiosity, coverage, and reconstruction objectives can conflict with task value, rewarding scans irrelevant to reaching the goal.For example, coverage can encourage scanning already irrelevant regions, while a direct route to the goal need not require looking behind.Source: §I · p. 1

I. INTRODUCTION

  • A single policy commands body twist and camera orientation without a sensing reward, so gaze control emerges from task pressure alone.The training terrains hide hazards from a level forward gaze, and an adaptive spawn curriculum scales difficulty as the policy improves.Source: §I · p. 1
  • LEAP uses gaze-invariant belief maps so observations are encoded consistently across viewpoints, avoiding a calibration penalty during gaze exploration.A batched heightmap ray-caster renders depth at on-policy training scale.Source: §I · p. 1
  • LEAP-trained navigation policies achieved 92.7% held-out success across five terrain families, within 4.6 percentage points of a ground-truth oracle given maps outright that never learns camera control.The policies transfer to a full-body quadruped in physics simulation over held-out terrains, steering an independently trained locomotion policy.Source: §I · p. 1

B. Visual Legged Locomotion

LEAP extends visual legged locomotion beyond passive, forward-facing sensing by making viewpoint choice a control decision. It represents observations in persistent egocentric belief maps and formulates navigation as a partially observable task in which the goal must be visually discovered.

B. Visual Legged Locomotion

  • Passive, body-fixed cameras suit linear courses where terrain unfolds ahead, but non-linear layouts can place hazards outside the forward frustum and require viewpoint selection.LEAP uses the same return to steer the body and camera.Source: B. Visual Legged Locomotion · p. 2

C. Viewpoint Calibration and Belief Maps

  • Depth images are back-projected through fixed camera geometry into gaze-invariant egocentric belief maps, so new viewpoints change observed cells but not their encoding.The map persists prior observations as local spatio-temporal memory, avoiding a recurrent state; its 2.5D representation cannot capture overhangs.Source: C. Viewpoint Calibration and Belief Maps · p. 2

III. PROBLEM STATEMENT

  • The navigation task is a POMDP in which the agent starts on unseen terrain, must reach an undisclosed goal, and controls a limited-field-of-view sensor to discover route features and the goal.The observation excludes the goal position; the goal is seen only when the sensor points toward it.Source: §III · pp. 2–3
  • Sensing actions carry no direct reward; reward depends on body position rather than sensor orientation.The problem abstracts the body as a planar twist on the terrain surface, with legged realization treated separately.Source: §III · pp. 2–3

A. Cost-to-Go on Anisotropic Terrain

The section defines a terrain-aware cost-to-go over feasible terrain, combining directional traversal costs through a Bellman optimality condition.

A. Cost-to-Go on Anisotropic Terrain

B. Reward

The reward combines cost-to-go-based progress with success, fall, and time terms. Its telescoping progress component gives no net reward to a probe-and-return detour, so gaze earns only through goal progress.

B. Reward

  • The cost-to-go supplies both the dense progress signal and success criterion, but is computed from ground-truth terrain and goal information unavailable to the actor.Source: B. Reward · p. 3
  • The reward combines dense progress shaping with a sparse success bonus, a fall penalty, and a constant time cost.Success is awarded when cost-to-go falls below rgoal = 0.5 m; cf = 2.5 and cτ = 0.002.Source: B. Reward · p. 3
  • A fall is a drop exceeding ∆hmax, while a rise exceeding that threshold blocks motion; reaching the goal, falling, timing out, or leaving terrain ends the episode.Source: B. Reward · p. 3
  • A probe-and-return detour nets exactly zero progress reward; gaze earns no direct reward and is rewarded only through progress toward the goal.The detour's only cost is the time it takes, through discount γ and cτ.Source: B. Reward · p. 3
  • Ablations found that neither the constant time cost nor the success bonus measurably affects the learned policy.Both terms are retained as trained.Source: B. Reward · p. 3

IV. METHOD

The method trains a navigation policy in a GPU-parallel environment and pairs it with a separate locomotion policy for quadruped execution.

IV. METHOD

  • The navigation policy is trained in a custom GPU-parallel environment of procedurally generated hazardous terrains, using heightmaps and precomputed cost-to-go maps for reward.Source: §IV · p. 4
  • The policy observes egocentric belief maps and robot state, and acts with a unicycle twist and pan-tilt velocities.Source: §IV · p. 4
  • A Transformer encoder with an attention mask implements an asymmetric actor-critic in one network; a separate locomotion policy executes the commanded twist on the quadruped.Source: §IV · p. 4

A. Terrain and Cost-to-Go Map

The terrain suite makes route hazards and goals difficult to resolve from a level forward gaze, while the observation combines depth-derived egocentric maps with robot state. The maps preserve both local height evidence and visual goal detections.

A. Terrain and Cost-to-Go Map

  • Five procedural terrain families hide route hazards from level forward gaze, requiring close-range inspection, search, or selection among bridges and platforms.Islands uses narrow crossings over moats; crests has depressed bridges; pillars creates alley searches; bridges includes an occluded decoy pit; decoys randomizes the goal side and clear bridge.Source: A. Terrain and Cost-to-Go Map · p. 4
  • The grid marks cells untraversable when local height range exceeds the threshold, then dilates obstacles by 0.15 m to seal passages narrower than the body.The agent is simulated as a point at its body center.Source: A. Terrain and Cost-to-Go Map · p. 4

B. Observation Space

  • Depth images update yaw-aligned egocentric belief maps whose cells encode height mean and uncertainty, ray hits, goal-marker hits, and visitation.The goal location enters the observation only through camera rays that intersect its marker; height evidence is accumulated from the depth-derived point cloud.Source: B. Observation Space · p. 4
  • The observation uses fine 0.1 m and coarse 0.6 m map grids; evidence decays before each update, relaxing stale cells toward a flat-ground prior.Unobserved cells read (0, 1.0 m, 0, 0, 0); the decay factors are 0.93 for fine and 0.99 for coarse maps.Source: B. Observation Space · p. 4

C. Action

The action combines locomotion commands with camera steering, making gaze control the only way to look away from the direction of travel.

C. Action

  • The action pairs a unicycle body twist with pan-tilt velocities; because body heading follows travel direction, camera control is the only way to look off-heading.The effective action is four-dimensional, with forward speed from −0.3 to 1.5 m/s and yaw rate limited to 1.5 rad/s.Source: C. Action · p. 5

D. Navigation Policy Architecture

The navigation policy uses a Transformer over belief-map and task tokens, with attention masking to keep privileged terrain information from the actor. A separate locomotion policy executes its twist commands while leaving hazard avoidance to navigation.

D. Navigation Policy Architecture

  • A shared three-stage Transformer policy tokenizes maps and robot state, applies a masked encoder, and decodes actor and critic outputs.The sequence contains 66 spatial and task tokens and uses a Transformer encoder over them.Source: D. Navigation Policy Architecture · p. 5
  • Each belief map becomes 16 patch tokens, while privileged ground-truth maps add 32 training-only tokens and a critic token carries terrain and goal information.Learned positional embeddings are added to map patches, and projection weights distinguish map types.Source: D. Navigation Policy Architecture · p. 5
  • Attention masking blocks the actor’s [CLS] and belief-map tokens from privileged critic and ground-truth tokens, while the critic attends to the full sequence.The actor and critic share the encoder, but the mask prevents privileged information reaching the actor through direct or multi-hop paths.Source: D. Navigation Policy Architecture · p. 5

E. Locomotion Policy

  • The locomotion actor receives a 19-dimensional T-shaped height scan that confines it to terrain compliance along the unicycle corridor, leaving hazard avoidance to navigation.Using the full scan made the locomotion actor overly conservative near pits and cliff edges; at deployment, the scan is sampled from the fine belief map.Source: E. Locomotion Policy · p. 5

F. Training and Implementation

The training pipeline uses a spawn-distance curriculum and a GPU depth renderer, while experiments compare passive, scripted, learned, and privileged camera-control variants. The renderer accelerates depth-based training, and LEAP’s gaze concentrates forward and down along travel.

F. Training and Implementation

  • Active gaze concentrates forward and down along travel, whereas Passive never moves and Sweep follows a pre-programmed trajectory.The distributions aggregate 10,000 held-out episodes per variant, with a traced episode on a shared pillars tile.Source: Figure 5 · p. 6
  • The spawn-distance curriculum raises difficulty after success and lowers it after struggling failure, with episode time budgets scaling from 40 s near the goal to 150 s at the farthest nominal spawn.Struggling failure means a fall or timeout without sufficient progress.Source: F. Training and Implementation · p. 6
  • 11.5 ± 3.0× throughput over IsaacLab ray-caster; replacing its renderer in yields 2.2× end-to-end wall-clock speed-up.The renderer produces exact depth on the discrete heightmap; the 2.5D representation precludes overhangs, and the renderer does not model robot-body self-occlusion.Source: F. Training and Implementation · p. 6

V. EXPERIMENTS

  • Experiments compare Passive, Sweep, Active (LEAP), and a privileged ground-truth oracle across goal-reaching, gaze strategy, and full-body quadruped transfer questions.The oracle is an upper bound rather than a baseline.Source: §V · p. 6

A. Protocol

On held-out terrains, LEAP’s learned gaze outperforms scripted sweeps and passive perception, while the value of gaze varies by terrain and spawn distance. The evaluation compares camera-control variants across unseen layouts and examines robustness as spawn distance changes.

A. Protocol

  • The protocol evaluates Passive, Sweep, Active, and a privileged GT oracle on held-out terrain, using five seeds and 2,000 episodes per terrain–variant pair.Each seed includes four randomized episodes on each of 100 unseen layouts; the Sweep camera follows a randomized-phase sinusoidal scan.Source: A. Protocol · p. 6, Table II · p. 7

B. Goal-Reaching on Held-Out Terrain

  • 92.7% mean success for Active versus 74.2% for Sweep and 34.5% for Passive, placing Active within 4.6 points of the GT oracle.The comparison covers 100 unseen layouts.Source: Table II · p. 7, B. Goal-Reaching on Held-Out Terrain · p. 7
  • Passive matches Active on pillars (97.7% vs. 98.8%) but performs poorly on crests and islands, where traversable crossings lie below a level gaze.An agent unable to look down cannot find those crossings.Source: B. Goal-Reaching on Held-Out Terrain · p. 7
  • Sweep recovers much of what Passive misses but lacks Active’s timing; on pillars it falls below Passive (75.0 vs. 97.7).Its indiscriminate gaze can miss a bridge at crossing time or pull away from visible forward obstacles.Source: B. Goal-Reaching on Held-Out Terrain · p. 7
  • Active overtakes Sweep beyond spawn distance d ≈ 0.35 and degrades more slowly; at d = 0.1, its 7.7% timeout rate versus 0.3% at d = 1 accounts for the success gap.Fall rates are similar at d = 0.1 and d = 1 (6.8% vs. 6.9%); the small-distance weakness reflects goal discovery and limited practice with steep upward gaze.Source: B. Goal-Reaching on Held-Out Terrain · p. 7, Figure 6 · p. 7

C. Emergent Gaze Strategies

LEAP’s gaze responds to the scene and belief state, while the privileged-map variant’s gaze becomes vestigial. In full-body simulation, the transfer ranking persists, though the paper notes limits in the training abstraction and observation representation.

C. Emergent Gaze Strategies

  • Active keeps most gaze time under the horizon with a forward pan, while Sweep scans broadly and symmetrically and Passive remains locked forward.The gaze statistics aggregate 10,000 episodes per variant; Active’s camera movement is attributed mainly to goal and terrain surveying.Source: C. Emergent Gaze Strategies · p. 7
  • With privileged maps, GT gaze drifts and snaps to the gimbal-limit corner, supporting the interpretation that gaze is learned when the policy relies on its belief.GT shares Active’s camera control but has privileged map access.Source: C. Emergent Gaze Strategies · p. 7

D. Full-Body Sim2Sim Transfer

  • In MuJoCo full-body transfer, the terrain-averaged ordering remains GT ≻ Active ≻ Sweep ≻ Passive, but absolute success rates are not comparable to Table II.The planar training abstraction removes leg contacts; in the full-body setting, some stumbles that would end planar episodes are recoverable.Source: D. Full-Body Sim2Sim Transfer · pp. 7–8

VI. CONCLUSION

  • 92.7% held-out success: LEAP exceeds scripted sweeps (74.2%) and passive perception (34.5%), and its navigation policy can steer a separately trained locomotion policy in full-body simulation.The conclusion reports the success figures for held-out terrains and describes the transfer as direct.Source: §VI · p. 8
  • The 2.5D belief representation cannot capture overhangs, and the navigation–locomotion interface remains frozen, with the policies trained independently.Joint training is left as future work.Source: §VI · p. 8

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