GLST: Global-Local Spatio-Temporal Memory Decomposition Framework for Online Chained-Goal Navigation

• Existing mapless reinforcement-learning and memory-based approaches predominantly assume a fixed navigation objective, leaving online goal changes outside their usual setting [7].Source: §1 · p. 1
• Goals may be redirected before completion or newly assigned after completion, and the agent may not be told which transition occurred.The setting requires using historical observations and interactions to handle both cases.Source: §1 · pp. 1–2
• Restarting after each update can compound failures, while unified memory may conflict between exploration of unseen regions and strategic revisitation.Source: §1 · p. 2
• GLST decomposes memory into global-local spatial and long-short temporal representations to preserve long-horizon context while supporting local adaptation.Source: §1 · p. 2
• The paper formulates online chained-goal navigation as an end-to-end partially observable problem with ambiguous goal evolution during execution.Source: §1 · p. 2
• The framework is evaluated in diverse-terrain simulations and real-robot deployments, with reported robust navigation under evolving goals and across horizons.Source: §1 · p. 2

• Long-horizon mapless methods use memory to capture history and improve robustness and exploration, but predominantly assume one static goal per episode [18].Source: §2 · p. 2
• Dynamic-goal methods commonly track persistent targets with changing states or locations, whereas this work allows discontinuous goal changes across arbitrary locations.Source: §2 · p. 2
• Multiple-goal methods typically optimize predefined goal ordering, routes, or waypoints, with explicit subgoal transitions and limited focus on long-horizon exploration and revisitation [31] [34].Source: §2 · p. 2
• The identified gap is how evolving objectives interact with navigation memory, including possible conflict between exploration and strategic revisitation.Source: §2 · p. 2

3.1 Problem Formulation

• The POMDP formulation allows redirection or new-goal emergence without explicit transition signals, requiring the policy to use observation histories of goals, environment structure, and robot states.A hierarchical controller has the navigation policy issue body-frame velocity commands for a low-level locomotion controller.Source: §3.1 · p. 3
• When optimal routes overlap visited regions, exploration and exploitation can induce opposing local gradient directions, motivating separated goal-conditioned memory encoders.The method uses subtrajectory-aware encoders to retain trajectory-specific context rather than mixing it in a unified representation.Source: §3.1 · pp. 3–4

3.2 Global-Local Spatio-Temporal Belief Learning (GLST)

• GLST decomposes beliefs into global-local spatial and long-short temporal representations for reasoning over traversability, environment structure, short-horizon dynamics, and long-horizon revisitation.Source: §3.2 · p. 4
• The local spatial belief encodes fine-grained terrain around the robot for reactive locomotion and local planning, while recurrent pose-conditioned accumulation and goal-conditioned attention produce a global spatial belief.Auxiliary heads predict map reconstruction, visibility, and confidence.Source: §3.2 · p. 4
• The framework combines the spatial beliefs with temporal beliefs, and trains locomotion and global spatial modules separately before navigation policy training.The training pipeline is staged, with pretrained low-level control and latent spatial representations supporting subsequent policy learning.Source: §3.2 · p. 5

3.3 Rewards and Curriculum

• The reward design includes goal-progress, exploration, stability, task-completion, collision, and excessive-roll terms, with the section focusing on progress and exploration rewards.The progress reward reinforces newly achieved closest distances; the exploration penalty uses a sparse visitation buffer maintained per goal segment.Source: §3.3 · p. 5

4.1 Simulation Experiments

• In maze simulation, GLST reduced the final failure rate from 39% to 21% as chained-goal success declined with longer sequences.The evaluation covers maze, pillar, pit, and multilevel stair terrains, with chains up to five goals.Source: §4.1 · p. 6, Figure 2 · p. 6
• SPL increased across the goal sequence despite comparable shortest-path distributions, indicating improved efficiency beyond differences in path difficulty.Timeout and collision were the dominant single-goal failure modes; excessive roll was rare.Source: §4.1 · p. 6, Figure 2 · p. 6
• The global spatial belief captured coarse traversability and major environmental layouts rather than fine-grained geometry, while preserving enough structure to navigate constrained passages.Local height maps were recursively integrated to update the global belief.Source: §4.1 · pp. 6–7
• GLST improves SR over SRU by over 14% absolute (23% relative) and over PCGrad by at least 19% absolute (41% relative), with higher SR and SPL than larger unified-memory models.The comparisons are summarized in Table 1(a); GLST also has substantially fewer timeout and collision failures.Source: Table 1 · p. 7, §4.1 · p. 7
• Removing the global spatial module degraded performance particularly on longer paths, while removing the local spatial module caused the largest drop.Temporal and exploration-reward ablations showed consistent trends supporting the architecture.Source: §4.1 · p. 7

4.2 Real-World Experiments

• Real-robot experiments used Spot in indoor and outdoor settings, including long-horizon chained goals with dead ends and dynamic obstacles.The policy relied on local observations while reconstructing coarse global traversability beliefs.Source: Figure 4 · p. 8, §4.2 · p. 8
• 86.1% success rate across 36 real-robot trials per method exceeded the best baseline, [2], by 11.1 percentage points in SR and 0.09 in SPL, at comparable speed (0.61 vs. 0.62 m/s).GLST also succeeded in dead-end and chained-goal scenarios where the baselines struggled.Source: §4.2 · p. 9

5 Limitations

• Because both spatial modules use the local height map, performance is sensitive to its quality; strong movable-object interactions can cause Spot SDK map drift and potentially saturate velocity commands.The paper also notes that the map representation does not correctly capture 3D structures such as overhangs.Source: §5 · p. 9
• Goal-conditioned memory is primarily empirically motivated, and rigorous analysis of conflicting memory gradients and their resolution remains future work.Source: §5 · p. 9
• Hierarchical training freezes a pretrained locomotion policy, making some failures difficult to attribute to navigation versus locomotion limitations.Joint training and sensitivity analysis across locomotion policies remain future directions.Source: §5 · p. 9
• Sim-to-real gaps persist: chairs and tables can be difficult to perceive reliably, and simulated map characteristics differ from real-robot perceptions.Source: §5 · p. 9

6 Conclusion

• GLST decomposes beliefs into global-local spatial and long-short temporal representations and combines this with goal-conditioned rewards to address conflicting exploration and revisitation requirements.Source: §6 · p. 9
• Simulation experiments across diverse terrains demonstrated improved long-horizon navigation performance.Source: §6 · p. 9
• Spot quadruped experiments demonstrated robust long-horizon chained-goal navigation indoors and outdoors, including dead ends and dynamic obstacles.The experiments reconstructed global spatial beliefs from local observations.Source: §6 · p. 9

A Estimation of Chained-Goal Success Rate Using Monte Carlo Simulation Under the Assumption of Independent-Goal Strategy

• The estimate assumes an independent-goal strategy in which the policy does not retain belief memory across goals; retaining-belief strategies are excluded.Source: A Estimation of Chained-Goal Success… · p. 14
• For a chain of length ng, Monte Carlo samples independently and uniformly draw single-goal success rates from the set reported in prior work.Source: A Estimation of Chained-Goal Success… · p. 14
• Figure 5 plots success rate by goal index for chains of one to five goals, showing upper single-goal rates and lower compounded rates under independent completion.The displayed estimates are adapted from prior-work results [2], [40], [41], [42], and [9].Source: Figure 5 · p. 14

B Proof of Conflicting Gradients in Online Chained-Goal Navigation

• Exploration rewards encourage trajectories to differ from visited regions using state-distribution divergence, while revisitation rewards encourage alignment with previously useful paths.The exploration formulation uses Jensen–Shannon divergence; revisitation minimizes state-distribution divergence.Source: B Proof of Conflicting Gradients in… · p. 15
• When a new goal’s optimal trajectory overlaps previously visited states, exploration and revisitation induce opposing gradient directions in that region.The analysis considers an overlapping reference trajectory and decomposes the objective into exploration and revisitation components.Source: B Proof of Conflicting Gradients in… · pp. 15–16
• A shared memory representation can receive conflicting learning signals: exploration discourages revisitation, whereas exploitation encourages revisiting useful states.This conflict arises around path overlaps under partial observability and evolving goals.Source: B Proof of Conflicting Gradients in… · pp. 15–16

C Global-Local Spatio-Temporal Belief Learning (GLST)

• GLST separates local reactive reasoning from persistent environment memory, and short-term motion dynamics from long-horizon trajectory history.The decomposition is intended to preserve local traversability detail alongside accumulated information useful for exploration, revisitation, and trajectory reuse.Source: C Global-Local Spatio-Temporal Belief… · p. 17, Figure 6 · p. 17
• Global spatial memory combines recurrent and projection-based components, with goal-conditioned attention selecting relevant regions from the accumulated map.The recurrent component captures long-range dependencies; attention pools spatial features according to the current goal.Source: C Global-Local Spatio-Temporal Belief… · p. 17
• Auxiliary heads supervise global spatial beliefs through terrain reconstruction, visibility prediction, and confidence estimation.Terrain reconstruction combines squared and absolute penalties to retain sharp terrain discontinuities; confidence targets reflect reconstruction quality.Source: C Global-Local Spatio-Temporal Belief… · p. 18
• Current, accumulated, and historical-snapshot trajectory memories distinguish active-goal motion from persistent history across chained-goal transitions.Current memory resets at a transition, accumulated memory continues across goals, and the snapshot preserves history from before the transition.Source: C Global-Local Spatio-Temporal Belief… · p. 19
• Training uses two-goal sequences with 4–10 m path lengths, while evaluation reaches 20 m and five goals; the learned policy generalizes beyond its training horizon.The passage attributes this generalization to preserving and reusing long-horizon spatial and temporal information.Source: C Global-Local Spatio-Temporal Belief… · p. 20

D Rewards and Curriculum

• Progress, exploration, collision, and time rewards have the largest reported impact on navigation performance and success; curriculum expands path lengths and terrain difficulty.Lateral-motion penalties and action-rate regularization primarily improve locomotion quality; the progress reward can still favor nearby gains in a locally suboptimal direction.Source: D Rewards and Curriculum · pp. 21–22

E Detailed Chained-Goal Evaluation Results

• Overall success rates decrease with path length and terrain complexity, while per-goal SR and SPL generally improve across chained stages.The authors suggest the per-goal pattern reflects improved navigation efficiency from trajectory reuse and accumulated spatial context.Source: E Detailed Chained-Goal Evaluation… · p. 23, Table 2 · p. 23

F Baseline Selection and Implementation

• The selected baselines include SRU for long-horizon mapless navigation and PCGrad for mitigating conflicting training gradients.SRU and PCGrad are reported as the stronger representatives of their respective baseline groups.Source: F Baseline Selection and Implementation · p. 24
• Unified-memory transformer and recurrent baselines use the same PPO framework, curriculum, and optimization settings as GLST, with comparable-or-greater parameter counts.Their unified input includes terrain, robot state, goal information, and navigation history, processed as a single memory representation.Source: F Baseline Selection and Implementation · pp. 24–25
• Table 3 reports navigation results over 1,000-rollout simulations across 10 seeds and identifies best SR/SPL and lowest failure rates.Failure modes listed are timeout, collision, and excessive roll.Source: Table 3 · p. 24

G Additional Real-World Experiments

• Figure 7 shows single-goal stair navigation and three-goal chained navigation indoors and in a forest.The appendix describes these as additional real-robot experiments.Source: Figure 7 · p. 26
• The Spot evaluation runs policy inference at 10 Hz, with elevation maps at 5 Hz and odometry at 50 Hz.Invalid height-scan values are filled using a BST-based nearest-neighbor search.Source: G Additional Real-World Experiments · p. 26
• The appendix identifies height-map constraints, sensor noise and latency, and unmodeled movable-object interactions as three sources of simulation-to-real gaps.These discrepancies contribute to performance degradation during real-robot operation.Source: G Additional Real-World Experiments · p. 26
• Height maps can misrepresent traversability: overhangs may register as obstacles despite clearance, while thin structures such as chair legs may be missed.These errors can produce inaccurate traversability estimates in real-world environments.Source: G Additional Real-World Experiments · p. 26
• Sensor differences, ROS communication latency, and odometry noise shift deployment conditions; matching simulation-level performance will likely require more domain randomization.The policy demonstrates robustness to moderate noise.Source: G Additional Real-World Experiments · p. 26
• Movable-object interactions are absent from simulation training, so contact-induced environmental changes can produce suboptimal behavior or failure.The policy is trained assuming obstacles remain static.Source: G Additional Real-World Experiments · p. 26