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Sampling-based Task and Kinodynamic Motion Planning under Semantic Uncertainty

Qi Heng Ho, Zachary N. Sunberg, Morteza Lahijanian

Abstract

This paper tackles the problem of integrated task and kinodynamic motion planning in uncertain environments. We consider a robot with nonlinear dynamics tasked with a Linear Temporal Logic over finite traces ($\ltlf$) specification operating in a partially observable environment. Specifically, the uncertainty is in the semantic labels of the environment. We show how the problem can be modeled as a Partially Observable Stochastic Hybrid System that captures the robot dynamics, $\ltlf$ task, and uncertainty in the environment state variables. We propose an anytime algorithm that takes advantage of the structure of the hybrid system, and combines the effectiveness of decision-making techniques and sampling-based motion planning. We prove the soundness and asymptotic optimality of the algorithm. Results show the efficacy of our algorithm in uncertain environments, and that it consistently outperforms baseline methods.

Sampling-based Task and Kinodynamic Motion Planning under Semantic Uncertainty

Abstract

This paper tackles the problem of integrated task and kinodynamic motion planning in uncertain environments. We consider a robot with nonlinear dynamics tasked with a Linear Temporal Logic over finite traces () specification operating in a partially observable environment. Specifically, the uncertainty is in the semantic labels of the environment. We show how the problem can be modeled as a Partially Observable Stochastic Hybrid System that captures the robot dynamics, task, and uncertainty in the environment state variables. We propose an anytime algorithm that takes advantage of the structure of the hybrid system, and combines the effectiveness of decision-making techniques and sampling-based motion planning. We prove the soundness and asymptotic optimality of the algorithm. Results show the efficacy of our algorithm in uncertain environments, and that it consistently outperforms baseline methods.

Paper Structure

This paper contains 19 sections, 3 theorems, 11 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Integrated Task and Motion Planning
  4. Reactive Planning and MPC
  5. Decision Making under Partial Observability
  6. Connection to SaBRS
  7. Problem Formulation
  8. Robot Dynamics and Task
  9. Label and Observation Uncertainty
  10. Planning Problem
  11. Approach
  12. Partially Observation Stochastic Hybrid System
  13. Anytime Sampling-based Bandit-guided Policy Iteration
  14. Policy Evaluation
  15. Policy Subtree Selection
  16. ...and 4 more sections

Key Result

Lemma 1

At iteration $i$, SaBPI produces a sound lower bound policy $\pi_i$, i.e., the reported value $V^{\pi_i} \leq V^{\pi^*}$, and executing $\pi_i$ results in at least that expected return. $\blacktriangleleft$$\blacktriangleleft$

Figures (4)

  • Figure 3: This example shows two possible motion trajectories in Example \ref{['ex: drone']}, where the observation quality is better near the fire than above the trees. In both (blue and orange) trajectories, the drone evolves in continuous time until it reaches $r_{1,2}^o$ or $r_{1,1}^o$, which triggers a guard $G_{T}$. Let both observations be $o = fire$ Then, it updates its memory state $m$, and updates its belief $b(e)$ of the environment state. The drone state evolves again until it reaches exit A, in which $G_{R}$ is triggered. This causes a belief update to the task DFA belief $b(q)$. In this example, the orange trajectory has higher probability of success than blue.
  • Figure 4: Benchmark Results of each algorithm for the four environments with a $60$ second time limit over $100$ trials.
  • Figure 5: C-Rock Sample with two different initial beliefs.
  • Figure 6: Drone Fire Detection Example: Exit A (green) and exit B (blue), fire sites (orange), obstacles (red). The yellow and gray hemispheres are observation regions.

Theorems & Definitions (16)

  • Example 1
  • Definition 1: $\textsc{ltl}_f\xspace$ Syntax ltlf
  • Example 2
  • Definition 2: PO-HMM
  • Definition 3: Motion Policy
  • Definition 4: PO-SHS with Persistent Observations
  • Definition 5: Belief-based Control Policy
  • Example 3
  • Remark 1
  • Remark 2
  • ...and 6 more