Source-linked AI summary
Sparse Planner: A Hybrid Planner for Efficient Sampling via a Conditional Variational Autoencoder
Wenguang Xu, Giovanni Lucente, Karem Mohamed, Richard Membarth
TL;DR
Dense sampling in sample-based motion planning increases computational cost, while maintaining real-time performance matters for autonomous-driving safety. SP uses a context-conditioned CVAE to generate sparse trajectory samples; it reports an eightfold sampling reduction and 2.5× speedup over FISS+ at comparable trajectory cost levels.
Problem
Dense sampling in SBMP raises computational consumption, while real-time planning performance directly affects autonomous-driving safety.
Source: §I · pp. 1–2Method
SP uses a CVAE to learn context-conditioned trajectory parameters and generate sparse, cost-biased samples.
Source: §I · p. 2, B. CVAE Training · p. 4Results
One-eighth the sampling number and a 2.5× speedup over FISS+ are reported at comparable trajectory cost levels, alongside fewer collision-induced planning failures.
Source: §I · p. 2Takeaways & Limitations
SP generates low-cost trajectory parameters with fewer samples, and its learned sampling performs particularly well with dynamic obstacles.
Source: §VI · p. 7
Abstract
from arXiv · showhide
Trajectory planning is a core component of autonomous driving systems, where real-time performance and solution quality directly affect safety and reliability. Sample-Based Motion Planning (SBMP) is widely adopted for its ability to approximate near-optimal solutions through parameter space sampling. However, achieving high-quality trajectories typically requires dense sampling, leading to substantial computational overhead and significant runtime variability in complex traffic scenarios. To address this limitation, we propose a Sparse Planner (SP) that improves sampling efficiency by learning the conditional relationship between scene context and effective trajectory parameters using a Conditional Variational Autoencoder (CVAE). By modeling the structure of high-quality sampling distributions, SP directly generates cost-effective samples in the parameter space, significantly reducing the required sampling density while preserving solution quality. Experimental results show that SP achieves lower trajectory cost than the state-of-the-art FISS+ planner while using only one-eighth of the sampling density. In addition, SP demonstrates improved distance-keeping capability in obstacle-rich scenarios and maintains reduced and more stable runtime characteristics, indicating enhanced computational efficiency and predictable runtime behavior.
I. INTRODUCTION
Dense sampling makes conventional SBMP computationally costly, motivating SP, which uses a CVAE to generate sparse, cost-biased samples while preserving trajectory quality. The paper situates this approach among planning methods that trade off feasibility, interpretability, and computational efficiency.
I. INTRODUCTION
- Dense parameter-space sampling causes combinatorial growth that limits the real-time applicability of conventional SBMP.The paper identifies efficient runtime with maintained reliability as a central motivation because planning performance affects driving safety.Source: §I · p. 1
- A CVAE learns context-conditioned trajectory parameters, replacing dense uniform sampling with sparse, cost-biased sampling that preserves trajectory quality.The learned distribution also concentrates samples in collision-free trajectory regions.Source: §I · p. 2
- SP uses one-eighth the sampling number and achieves a 2.5× speedup over FISS+ at comparable trajectory cost levels, while decreasing collision-induced planning failures.The paper also reports lower trajectory cost as a contribution.Source: §I · p. 2
II. BACKGROUND
- Trajectory planning is formulated as minimizing trajectory cost subject to initial-state, goal-region, collision-free-space, and vehicle-dynamics constraints.The paper describes graph-, sampling-, optimization-, and learning-based planning categories.Source: §II · p. 2
- Graph planners simplify vehicle dynamics, optimization planners have difficult-to-predict runtimes, and learning-based planners may lack explicit safety constraints and interpretability.These trade-offs motivate a sampling-based approach that retains explicit constraint handling.Source: §II · p. 2, §I · p. 2
- FOP samples interpretable terminal lateral offsets and target speeds in Frenét coordinates, then constructs, checks, and scores feasible trajectories.Its independent candidate generation and evaluation support parallel computation.Source: §II · p. 2
A. Heuristics-Driven Sampling
Prior sampling approaches use heuristic search or learned distributions to reduce exhaustive sampling, each with constraints on refinement, scaling, or generality. SP builds on learned conditioned sampling and extends it to autonomous-driving traffic scenes using BEV conditioning.
A. Heuristics-Driven Sampling
- FISS+ combines discretized global search with gradient-descent refinement to reduce discretization-induced suboptimality and more accurately approximate the global optimum.FISS first prioritizes candidates using estimated costs and a history-based heuristic.Source: A. Heuristics-Driven Sampling · p. 3
B. Deep-Learning for Learning Samples Distribution
- Learned sampling methods bias proposals toward feasible or task-relevant regions, but prior approaches require informative exemplars, geometric post-processing, sequential inference, or discretized terminal-state lattices.The approaches described include GMMs, rasterized-scene GANs, transformers, and LF-Net.Source: B. Deep-Learning for Learning Samples… · p. 3
- SP builds on CVAE-conditioned sampling demonstrated in robotics and extends it to autonomous driving, using BEV conditioning for arbitrary traffic scenarios rather than predefined maneuvers.The cited robotics tasks include static obstacle avoidance, path planning, and overtaking.Source: B. Deep-Learning for Learning Samples… · p. 3
IV. METHODOLOGY
SP conditions a CVAE on ego-aligned BEV sequences to generate trajectory parameters, then uses the existing feasibility and cost-evaluation pipeline to select a trajectory. The training data pairs FOP-selected terminal parameters with BEV sequences from CommonRoad scenarios.
IV. METHODOLOGY
- Three stacked ego-aligned BEV frames condition the CVAE, which generates Frenét trajectory parameters that are transformed into global coordinates for planning.The square BEV covers 100 m × 100 m, and the number of generated samples is configurable.Source: §IV · p. 3
- Generated trajectories undergo the same feasibility checks, collision avoidance, and cost evaluation across planners; FOP provides a fallback if SP produces no feasible trajectory.The fallback activation probability is reported as negligible.Source: §IV · p. 3
A. Dataset Recording
- FOP’s dense uniform sampling supplies CVAE training targets: selected optimal trajectories yield terminal parameters paired with BEV inputs from CommonRoad scenarios.The experiments use 19,040 samples per planning cycle and 3,500 scenarios split into training, validation, and test sets; the test set contains 350 scenarios.Source: A. Dataset Recording · pp. 3–4
IV. METHODOLOGY
- At inference, the planner samples latent variables and decodes trajectory parameters, evaluates the resulting candidates, falls back to FOP if none are feasible, and returns the minimum-cost trajectory.The algorithm takes vehicle-centric BEV conditioning with lanes, obstacles, and a reference path as input.Source: A. Dataset Recording · p. 4
B. CVAE Training
The CVAE learns a BEV-conditioned distribution over optimal trajectory parameters, using an encoder to approximate latent posteriors and a decoder to model parameter likelihoods.
B. CVAE Training
- The model learns context-conditioned distributions over parameter-space samples containing optimal trajectories, with the BEV sequence representing context.The encoder approximates the posterior conditioned on both the sample and context; the decoder models sample likelihood conditioned on the latent representation and context.Source: B. CVAE Training · p. 4
- The encoder maps each sample to a multivariate normal latent distribution, and reparameterization enables differentiable sampling for encoder gradients.The latent sample is formed from the encoder’s mean and standard deviation with Gaussian noise.Source: B. CVAE Training · p. 4
- The generative model factors the joint distribution into a decoder likelihood and a latent prior, with the prior conditioned on context.The decoder models the sample distribution given the latent representation and context.Source: B. CVAE Training · p. 4
- Training jointly optimizes the encoder, decoder, and prior to reduce reconstruction error and the divergence between approximate and true posteriors.The ELBO objective is reformulated using the context-conditioned prior, and the loss also includes an MSE term between generated and ground-truth samples.Source: B. CVAE Training · p. 4
C. CVAE Architecture
The architecture conditions trajectory-parameter generation on BEV context, using a CVAE whose inference path samples from a context-conditioned prior and reuses the training decoder.
C. CVAE Architecture
- Three conditioning frames are stacked into a (3, 256, 256) tensor, normalized, and processed by pretrained ResNet18 into (64, 32) tokens; input x = (d, ˙s, T) is tokenized as (16, 32).Learned positional encoding vectors are added to both token sequences.Source: C. CVAE Architecture · p. 4
- During training, encoder and decoder map optimal-parameter distributions conditioned on BEV embeddings through a latent space; inference samples from the prior and uses the same decoder.The figure depicts the encoder being replaced by the prior during inference.Source: Figure 2 · p. 5, C. CVAE Architecture · p. 5
- The CVAE loss adds a generative MSE term to the negative ELBO, while its prior is conditioned on context rather than modeled as standard normal.The added loss term reduces MSE by about 14%, and the context-conditioned prior yields an additional 10% reduction.Source: C. CVAE Architecture · p. 5
V. EVALUATION
The evaluation records per-cycle runtime and total trajectory cost across 350 scenarios, with SP using FOP as a fallback when it finds no feasible trajectory.
V. EVALUATION
- Across 350 scenarios, the evaluation aggregates average trajectory cost, runtime per planning cycle, and SP’s normalized fallback rate.SP falls back to FOP when no feasible trajectory is found; the fallback uses 125 FOP samples.Source: §V · p. 5
- Runtime excludes the preceding module that supplies CVAE input images, so the reported SP runtime does not include that module’s computation.Runtime is recorded per planning cycle during simulation.Source: §V · p. 5
- Trajectory cost uses the FISS+ cost function, weighted to emphasize ride comfort and safety through acceleration, jerk, obstacle proximity, and lane-center deviation.The stated weights include wV=0.1, wA=10, wJ=10, wD=100, wdist=0.1, and wT=1.Source: §V · p. 5
A. Performance Analysis
SP achieves lower trajectory cost than FOP and FISS+ at comparable sampling sizes, while its fallback rate falls as sample count increases. The experiments also identify N = 64 as a trade-off point between runtime, trajectory cost, and reliability.
A. Performance Analysis
- Of 350 scenarios, FISS+ fails in 82, while FOP and SP with FOP fallback complete all 350; cost comparisons use the 268 common-success scenarios.FISS+’s failure rate remains around 20% as its sample count increases beyond N = 216.Source: A. Performance Analysis · p. 6
- Increasing N generally reduces trajectory cost while increasing runtime; SP and FOP scale approximately linearly, whereas FISS+ runtime grows more slowly.FISS+’s heuristic prioritization avoids evaluating all samples.Source: A. Performance Analysis · p. 6
- With N = 1, SP already achieves lower trajectory cost than FOP and FISS+ at N = 125.The comparison indicates that the CVAE generates samples associated with low-cost trajectory parameters.Source: A. Performance Analysis · p. 6
- SP’s fallback rate falls from 18.9% at N = 1 to 4.0% at N = 64, then does not decrease further.The remaining fallback cases are attributed to long-tail scenarios the model fails to map to a correct optimal-parameter distribution.Source: A. Performance Analysis · p. 6
- At N = 64, SP runtime is 47 ms versus 82 ms at N = 125, with marginal cost improvement; N = 64 is selected as the trade-off point.Generating 64 samples takes an average of 7 ms of CVAE inference per planning cycle.Source: A. Performance Analysis · p. 6
B. Qualitative Case Study
Two representative scenarios illustrate SP’s obstacle-clearance behavior and its performance in a challenging drive-brake-drive maneuver. In both cases, SP maintains greater distance from the leading obstacle or vehicle.
B. Qualitative Case Study
- In the lane-following case, SP plans the safest trajectories at time steps 50 and 80, with greater clearance from the dynamic obstacle.The paper attributes this behavior to training the CVAE on 2,450 FOP-planned scenarios with many samples.Source: B. Qualitative Case Study · p. 6
- In the drive-brake-drive case, FISS+ fails at time step 63 after insufficient deceleration, while SP and FOP complete the scenario.SP has lower trajectory cost and keeps greater distance from the front vehicle, particularly at time step 100.Source: B. Qualitative Case Study · p. 6
C. Deterministic Runtime Performance
Across scenarios, SP shows a compact, low-variance runtime distribution, unlike FISS+’s broad spread. The reported worst-case FISS+ runtimes illustrate that variability.
C. Deterministic Runtime Performance
- Two FISS+ instances exceed 175 ms mean runtime and 300 ms runtime standard deviation in the worst-case scenarios.These high-variability cases are contrasted with SP’s clustered distribution.Source: C. Deterministic Runtime Performance · p. 6
- SP’s compact, low-variance runtime distribution contrasts with FISS+’s broad spread across scenarios, supporting SP’s more deterministic runtime performance.The paper describes SP as more suitable for real-time autonomous driving systems.Source: C. Deterministic Runtime Performance · pp. 6–7, Figure 5 · p. 7
- Each Fig. 5 point represents a scenario’s average runtime and standard deviation across planning cycles.The plot compares these two runtime measures for FISS+ and SP across 268 scenarios.Source: Figure 5 · p. 7
VI. CONCLUSION
The conclusion presents SP as a CVAE-based sampling framework that generates low-cost trajectory parameters with fewer samples. It highlights dynamic-obstacle performance and identifies real-sensor-stack integration as future work.
VI. CONCLUSION
- SP uses a context-conditioned CVAE sampling strategy to generate low-cost trajectory parameters with significantly fewer samples and reduced runtime.The conclusion describes it as a hybrid planning framework that samples efficiently in parameter space.Source: §VI · p. 7
- The learned sampling mechanism performs particularly well in scenarios with dynamic obstacles, where contextual understanding is crucial.Source: §VI · p. 7
- BEV conditioning is described as compatible with real sensor setups, and future work could integrate SP with a real sensor stack.The conclusion also says the fallback mechanism ensures completeness in case of failure.Source: §VI · p. 7