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LaPlaSS: Latent Space Planning for Stochastic Systems

Marlyse Reeves, Brian C. Williams

TL;DR

LaPlaSS tackles risk-bounded trajectory planning for stochastic agents with learned dynamics by combining a generate-and-test loop with latent-space planning. A variational autoencoder learns an accurate stochastic dynamics model and a linear latent dynamic, enabling convex optimization in latent space to generate candidate trajectories. A trajectory validator constructs a probabilistic flow tube via extensive sampling and fast risk bounds (Liu-Tang-Zhang) to iteratively refine safety constraints until a safe plan is found. The approach yields substantial planning speedups (approximately 11s vs >120s in a baseline) while maintaining bounded risk, demonstrated on both synthetic nonlinear dynamics and real-world drone data.

Abstract

Autonomous mobile agents often operate in hazardous environments, necessitating an awareness of safety. These agents can have non-linear, stochastic dynamics that must be considered during planning to guarantee bounded risk. Most state of the art methods require closed-form dynamics to verify plan correctness and safety however modern robotic systems often have dynamics that are learned from data. Thus, there is a need to perform efficient trajectory planning with guarantees on risk for agents without known dynamics models. We propose a "generate-and-test" approach to risk-bounded planning in which a planner generates a candidate trajectory using an approximate linear dynamics model and a validator assesses the risk of the trajectory, computing additional safety constraints for the planner if the candidate does not satisfy the desired risk bound. To acquire the approximate model, we use a variational autoencoder to learn a latent linear dynamics model and encode the planning problem into the latent space to generate the candidate trajectory. The VAE also serves to sample trajectories around the candidate to use in the validator. We demonstrate that our algorithm, LaPlaSS, is able to generate trajectory plans with bounded risk for a real-world agent with learned dynamics and is an order of magnitude more efficient than the state of the art.

LaPlaSS: Latent Space Planning for Stochastic Systems

TL;DR

LaPlaSS tackles risk-bounded trajectory planning for stochastic agents with learned dynamics by combining a generate-and-test loop with latent-space planning. A variational autoencoder learns an accurate stochastic dynamics model and a linear latent dynamic, enabling convex optimization in latent space to generate candidate trajectories. A trajectory validator constructs a probabilistic flow tube via extensive sampling and fast risk bounds (Liu-Tang-Zhang) to iteratively refine safety constraints until a safe plan is found. The approach yields substantial planning speedups (approximately 11s vs >120s in a baseline) while maintaining bounded risk, demonstrated on both synthetic nonlinear dynamics and real-world drone data.

Abstract

Autonomous mobile agents often operate in hazardous environments, necessitating an awareness of safety. These agents can have non-linear, stochastic dynamics that must be considered during planning to guarantee bounded risk. Most state of the art methods require closed-form dynamics to verify plan correctness and safety however modern robotic systems often have dynamics that are learned from data. Thus, there is a need to perform efficient trajectory planning with guarantees on risk for agents without known dynamics models. We propose a "generate-and-test" approach to risk-bounded planning in which a planner generates a candidate trajectory using an approximate linear dynamics model and a validator assesses the risk of the trajectory, computing additional safety constraints for the planner if the candidate does not satisfy the desired risk bound. To acquire the approximate model, we use a variational autoencoder to learn a latent linear dynamics model and encode the planning problem into the latent space to generate the candidate trajectory. The VAE also serves to sample trajectories around the candidate to use in the validator. We demonstrate that our algorithm, LaPlaSS, is able to generate trajectory plans with bounded risk for a real-world agent with learned dynamics and is an order of magnitude more efficient than the state of the art.
Paper Structure (17 sections, 13 equations, 5 figures, 1 algorithm)

This paper contains 17 sections, 13 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Approach Overview
  4. Planning Algorithm
  5. Model Learning
  6. Trajectory Validation
  7. Generating a PFT
  8. Fast Risk Assessment
  9. Computing Safety Constraints
  10. Trajectory Planning with Learned Models
  11. Learning Accurate Dynamics
  12. Learning Approximate Linear Dynamics
  13. Planning in the Latent Space
  14. Results
  15. Planning Algorithm Performance
  16. ...and 2 more sections

Figures (5)

  • Figure 1: High-level Diagram of Approach
  • Figure 2: (left) Trajectories sampled from learned dynamics model to fit a sequence of distributions that form the probabilistic flow tube. (right) Illustration of safety constraint computation. (a) The "riskiest" state in the candidate trajectory after risk assessment using the PFT. (b) Computing the safety constraint using the confidence ellipse of the distribution at the riskiest state. (c) New candidate trajectory constrained by the safety constraint computed in the previous iteration.
  • Figure 3: (left) Architecture for accurate learned dynamics. (right) Architecture for approximate linear latent dynamics.
  • Figure 4: Planner comparison. (left) Example trajectory generated by weiqiao2022's approach. (right) Example trajectory by our approach.
  • Figure 5: Trajectory planned for the Blackbird quadrotor using learned dynamics. The green and red circles are the initial state and goal state. The purple ellipsoid is an obstacle.