Source-linked AI summary
Learning Sampling Distributions for Robot Motion Planning
Brian Ichter, James Harrison, Marco Pavone
TL;DR
Sampling-based motion planning can waste samples in state-space regions irrelevant to a particular solution, despite robotic motion often being confined to small regions. The paper learns problem-conditioned sample distributions with a conditional variational autoencoder from demonstrations, then uses them to bias sampling. Across planning problems, the method achieves approximately an order of magnitude improvement in success rate and cost over uniform sampling while maintaining sampling-based planning guarantees.
Problem
Uniform sampling may exhaustively cover state spaces even when environments, dynamics, or implicit constraints restrict useful motion to small regions.
Method
A conditional variational autoencoder learns sample distributions from successful plans and prior experience, generating problem-conditioned samples for promising state-space regions.
Results
Approximately an order of magnitude improvement in success rates and path costs over uniform sampling was demonstrated across diverse planning problems.
Takeaways & Limitations
The learned sampling approach can focus planning on relevant state-space regions while remaining applicable to arbitrary systems and preserving completeness and asymptotic optimality.
Takeaways & Limitations
Environment conditioning was demonstrated only on relatively small, planar problems, and scaling it to large, high-dimensional problems is challenging.
Abstract
from arXiv · showhide
A defining feature of sampling-based motion planning is the reliance on an implicit representation of the state space, which is enabled by a set of probing samples. Traditionally, these samples are drawn either probabilistically or deterministically to uniformly cover the state space. Yet, the motion of many robotic systems is often restricted to "small" regions of the state space, due to, for example, differential constraints or collision-avoidance constraints. To accelerate the planning process, it is thus desirable to devise non-uniform sampling strategies that favor sampling in those regions where an optimal solution might lie. This paper proposes a methodology for non-uniform sampling, whereby a sampling distribution is learned from demonstrations, and then used to bias sampling. The sampling distribution is computed through a conditional variational autoencoder, allowing sample generation from the latent space conditioned on the specific planning problem. This methodology is general, can be used in combination with any sampling-based planner, and can effectively exploit the underlying structure of a planning problem while maintaining the theoretical guarantees of sampling-based approaches. Specifically, on several planning problems, the proposed methodology is shown to effectively learn representations for the relevant regions of the state space, resulting in an order of magnitude improvement in terms of success rate and convergence to the optimal cost.
1 Introduction
Sampling-based motion planning traditionally uses uniform samples, but robotic motion often occupies small, complex regions where non-uniform sampling could accelerate finding high-quality solutions. The paper learns conditional sample distributions from demonstrations to focus sampling on promising regions while retaining sampling-based planning guarantees.
- Motivation: Uniform sampling provides arbitrarily accurate state-space representations in the limit, but may require many samples to cover promising regions.SBMP uses samples and black-box local connection checks to represent feasible spaces.
- Motivation: Robotic motion is often restricted to small regions by environments, system dynamics, or implicit constraints.Examples include narrow passageways, stable bipedal configurations, loop closures, and collision avoidance among multiple robots.
- Method: The proposed method uses a conditional variational autoencoder trained on successful plans and prior experience to learn complex, problem-conditioned sample distributions.Latent-space samples are projected into promising state-space regions using information such as initial state, goal region, and obstacles.
- Method: The methodology is designed for arbitrary systems and problems, scales to high dimensions, and preserves completeness and asymptotic optimality.It can incorporate system-specific and problem-specific constraints while remaining compatible with sampling-based planners.
- Results: Across diverse planning problems, learned sampling yields approximately an order of magnitude improvement in success rates and path costs over uniform sampling.The extended version also adds experiments on generalization, iterative retraining, and multirobot planning.
2 Related Work
Non-uniform sampling methods include heuristics, informed sampling, adaptive sampling, and learning-based approaches. They differ in when distributions change, what information they use, and how broadly they generalize across planning problems.
- Heuristic methods: Heuristic methods use workspace information to choose a mostly offline sampling distribution, but may not transfer beyond their designed environments.Examples include decomposition techniques and medial-axis approximations.
- Informed sampling: Informed sampling changes the distribution online using the current best trajectory, but cannot refine sampling before a feasible trajectory is found.Several informed methods reject samples that cannot improve the current best solution and are restricted to geometric planning.
- Adaptive sampling: Adaptive sampling changes distributions during a planning problem using information acquired from previous samples.Prior approaches use utility functions, experience graphs, local connectivity, or free-space classification, but may not generalize to arbitrary problems or combine full-state and external information.
- Learned sampling: Learned sampling uses knowledge from previous planning problems to improve samples without waiting for information from the current problem.The paper’s approach is an offline, learning-based method.
- Learned sampling: Workspace discretization can reduce configuration-space dimensionality effects but may degrade performance relative to learning distributions directly in state space.This limitation motivates state-space sampling distributions for complex planning settings.
3 Problem Statement
The paper formulates optimal motion planning as finding a lowest-cost feasible trajectory from an initial state to a goal region while avoiding obstacles. Because general formulations can be computationally difficult, sampling-based methods provide an approximate solution strategy for complex systems.
- Problem definition: In the geometric formulation, the state space is X = [0, 1]^d, with obstacle space Xobs, free space Xfree, initial state xinit, and goal region Xgoal.The path is a continuous function s: [0, 1] → R^d, and cost is Euclidean distance.
- Problem definition: Optimal motion planning seeks a feasible path with minimum cost from an initial state to a goal region, or reports failure if none exists.Feasibility requires collision avoidance, the specified initial condition, and termination in the goal region.
- Problem scope: Motion-planning formulations may include kinematic, differential, or more complex system constraints.The paper treats geometric planning as the simplest version of a broader constrained planning problem.
- Problem scope: General motion planning is PSPACE-complete, motivating approximate methods for efficient solution of complex, high-dimensional problems.Sampling-based motion planning is identified as particularly successful for such settings.
4 Learning-Based Sample Distributions
The methodology learns a conditional sampling distribution from demonstrations, then combines generated samples with uniform samples for new planning problems. A CVAE provides the learned distribution while auxiliary uniform sampling preserves SBMP’s theoretical guarantees.
- Offline learning: The method trains a CVAE on demonstrations and prior robot experience to model sample distributions conditioned on planning-problem information.Training data can include successful motion plans, previous trajectories, human demonstrations, or other sources describing system operation.
- Conditional generation: The CVAE represents conditional sample densities with an encoder and decoder, then generates approximate samples by drawing latent variables from N(0, I).The decoder maps latent samples and conditioning information into state-space samples.
- Online conditioning: New planning problems are encoded through conditioning variables that may include the initial state, goal region, or occupancy-grid workspace obstacles.The online phase forms the tuple (Xfree, xinit, Xgoal) into a conditioning variable y.
- Online sampling: The online sampler generates λN learned samples and (1−λ)N auxiliary samples before running a sampling-based planner such as PRM∗, FMT∗, or RRT∗.The auxiliary sampler is uniform, and experimentation found λ = 0.5 to provide a satisfactory balance.
- Theoretical guarantees: Uniform auxiliary sampling preserves probabilistic completeness and asymptotic optimality by ensuring arbitrarily faithful coverage through the (1−λ)N uniform samples.The guarantees are obtained by adjusting the sample count in the standard results to the number of uniform samples.
5 Numerical Experiments: Performance and Scalability
Across geometric, spacecraft, narrow-passage, and articulated-arm problems, learned sampling distributions improve planning convergence while representing problem-relevant state-space structure. The experiments combine the learned method with multiple sampling-based planners and report strong performance across systems and conditions.
- Experimental scope: The experiments evaluate learned sampling with FMT∗, BIT∗, and GPU implementations of PRM∗ and GMT∗ across varied robotic planning problems.The evaluation includes geometric planning, spacecraft debris recovery, workspace-conditioned narrow passages, and articulated-arm scenarios.
- Workspace-conditioned planning: The method learns distributions conditioned on initial state, goal region, and obstacle occupancy grids for environments containing multiple narrow passages.The broader experiments vary conditioning information and system complexity, including workspace representations and dynamics-driven sampling.
- Geometric planning comparisons: In geometric planning, learned sampling finds solutions nearly as often as alternatives but reaches significantly better solutions within the same time.With FMT∗, it reaches within 5% of the best solution almost immediately; with BIT∗, it performs at least as well as the other strategies.
- Spacecraft debris recovery: The spacecraft distributions form an ellipsoid between the initial state and goal, favor goal-directed velocities, and concentrate arm angles at a few values.These patterns reflect obstacle accommodation, directed motion, and reduced arm movement where arm motion carries substantial cost.
- Spacecraft debris recovery: Approximately an order of magnitude separates learned from uniform sampling in finding spacecraft solutions, while learned samples converge almost immediately to within a few percentage of optimal.After 10,000 samples, uniform sampling remains more than 60% from optimal, and learned distributions also show smaller variance.
- Limitations and safeguards: Learned distributions can sometimes cut corners and produce infeasible trajectories, but uniform sampling and SBMP guarantees provide a fallback for these failures.The paper presents learning as an attempt to solve the problem directly while retaining a theoretically sound sampling-based algorithm.
- Articulated-arm planning: In an articulated-arm problem with unintuitive optimal sample placement, convergence results show similar performance increases.This extends the reported gains to a setting where useful sampling locations are not obvious in the state space.
6 Numerical Experiments: Extensions, Data Sources, Generalization, and Hyperparameter Selection
The experiments examine sampling-fraction choices, structured and generalized learned distributions, iterative retraining, multirobot planning, and human-demonstration data. Learned sampling improves performance broadly, but training-data quality and distribution mismatch remain important boundaries.
- 6.1 Fraction of Learned Samples (λ): A 50% learned-sample fraction was selected because it performed well across convergence, success rate, and runtime.Fractions at least 25% converged similarly; fractions above 75% sometimes missed important regions, while runtime rose quickly above 50%.
- 6.1 Fraction of Learned Samples (λ): Learned samples typically achieved rapid convergence within a few hundred samples, while an auxiliary sampler filled gaps on slower problems.The authors suggest increasing uniform sampling over time as a possible improvement, especially with limited training data.
- 6.2 Structured Distributions: Learning multiple dependent samples together enforced dispersion between samples and extended the method to structured batch sampling.The distributions were learned from solution trajectories containing three or more samples.
- 6.3 Varied Obstacle Density: Training and testing across maze complexities showed that all learned distributions outperformed uniform sampling in success rate and normalized cost.Matching training and testing complexity generally performed best, while low-complexity training tested on high-complexity mazes performed worst.
- 6.4 Iterative Training of CVAE: Multirobot planning exposed a training-data challenge because uniform-sampling trajectories were low quality and failed to capture synchronized near-optimal motion.After 5000 samples, the best uniformly generated trajectory had normalized cost greater than 1.5.
- 6.5 Human Demonstration: Human demonstrations produced a learned lane-changing distribution that captured collision avoidance, lane preferences, forward velocity, and maneuver-specific states.Because uniform sampling could not reach this problem and no two-point boundary-value solver was available, evaluation was qualitative.
7 Discussion and Conclusions
The paper concludes that CVAE-based learned sampling can bias motion-planning samples toward valid or desirable state subspaces while retaining sampling-based planning guarantees. It also identifies environment-conditioning scalability and training-data requirements as directions for continued work.
- Conclusions: The methodology learns CVAE-based sampling distributions conditioned on planning information and improves cost and success rate over uniform sampling across multiple systems.The approach is presented as general, extensible, applicable to arbitrary systems, and compatible with completeness and asymptotic optimality.
- Future Work: Future extensions include semantic workspace conditioning, larger dependent sample sets, and methods for systems whose valid configurations lie on lower-dimensional structures.The paper specifically identifies reduced sample independence and sample sets larger than 1000 as possible extensions.
- Discussion and Limitations: Workspace-map conditioning was demonstrated only on relatively small planar problems, and its conditioning-variable count grows exponentially with grid resolution and problem dimensionality.The authors propose lower-dimensional environment representations or adaptive conditioning based on collision-tested samples or tree state.
- Application in Practice: The practical workflow recommends training on approximately one hundred thousand optimal motion plans and combining learned with uniform samples online.A 50-50 learned-to-uniform split was reported as most effective.