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Robust Predictive Motion Planning by Learning Obstacle Uncertainty

Jian Zhou, Yulong Gao, Ola Johansson, Björn Olofsson, Erik Frisk

TL;DR

The paper tackles safe motion planning under obstacle uncertainty by online learning the obstacles' intended control sets, reducing the conservatism of worst-case predictions. It introduces a linear-programming based method to learn hat{\mathbb{U}}_t^s from observed actions, and uses forward reachability to predict obstacle occupancy, which feeds a robust MPC that computes a safe reference trajectory for the ego system. The approach is validated through simulations and hardware experiments in reach-avoid scenarios, showing improved safety and feasibility relative to deterministic MPC and reduced conservatism relative to RMPC, without requiring prior knowledge of obstacle uncertainty distributions. The work offers real-time applicable techniques for uncertain, dynamic environments and suggests future integration with map-informed and interaction-aware prediction frameworks for more complex traffic scenarios.

Abstract

Safe motion planning for robotic systems in dynamic environments is nontrivial in the presence of uncertain obstacles, where estimation of obstacle uncertainties is crucial in predicting future motions of dynamic obstacles. The worst-case characterization gives a conservative uncertainty prediction and may result in infeasible motion planning for the ego robotic system. In this paper, an efficient, robust, and safe motion-planing algorithm is developed by learning the obstacle uncertainties online. More specifically, the unknown yet intended control set of obstacles is efficiently computed by solving a linear programming problem. The learned control set is used to compute forward reachable sets of obstacles that are less conservative than the worst-case prediction. Based on the forward prediction, a robust model predictive controller is designed to compute a safe reference trajectory for the ego robotic system that remains outside the reachable sets of obstacles over the prediction horizon. The method is applied to a car-like mobile robot in both simulations and hardware experiments to demonstrate its effectiveness.

Robust Predictive Motion Planning by Learning Obstacle Uncertainty

TL;DR

The paper tackles safe motion planning under obstacle uncertainty by online learning the obstacles' intended control sets, reducing the conservatism of worst-case predictions. It introduces a linear-programming based method to learn hat{\mathbb{U}}_t^s from observed actions, and uses forward reachability to predict obstacle occupancy, which feeds a robust MPC that computes a safe reference trajectory for the ego system. The approach is validated through simulations and hardware experiments in reach-avoid scenarios, showing improved safety and feasibility relative to deterministic MPC and reduced conservatism relative to RMPC, without requiring prior knowledge of obstacle uncertainty distributions. The work offers real-time applicable techniques for uncertain, dynamic environments and suggests future integration with map-informed and interaction-aware prediction frameworks for more complex traffic scenarios.

Abstract

Safe motion planning for robotic systems in dynamic environments is nontrivial in the presence of uncertain obstacles, where estimation of obstacle uncertainties is crucial in predicting future motions of dynamic obstacles. The worst-case characterization gives a conservative uncertainty prediction and may result in infeasible motion planning for the ego robotic system. In this paper, an efficient, robust, and safe motion-planing algorithm is developed by learning the obstacle uncertainties online. More specifically, the unknown yet intended control set of obstacles is efficiently computed by solving a linear programming problem. The learned control set is used to compute forward reachable sets of obstacles that are less conservative than the worst-case prediction. Based on the forward prediction, a robust model predictive controller is designed to compute a safe reference trajectory for the ego robotic system that remains outside the reachable sets of obstacles over the prediction horizon. The method is applied to a car-like mobile robot in both simulations and hardware experiments to demonstrate its effectiveness.
Paper Structure (25 sections, 2 theorems, 24 equations, 15 figures, 5 tables)

This paper contains 25 sections, 2 theorems, 24 equations, 15 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Uncertainty Prediction
  4. Uncertain-Aware Motion Planning
  5. Problem Statement
  6. Notations
  7. Modeling of Ego System and Surrounding Obstacles
  8. Research Problem
  9. Learning Obstacle Uncertainty
  10. Learning Intended Control Set $\tilde{\mathbb{U}}_t^s$
  11. Computing $\hat{\mathbb{U}}_t^s$ with Low Complexity
  12. Moving-Horizon Approach
  13. Online Recursion
  14. Forward Reachability Analysis Based on $\hat{\mathbb{U}}_t^s$
  15. Performance Evaluation
  16. ...and 10 more sections

Key Result

Lemma 4.1

For any $v \in \mathbb{U}^s$, $\bm{\theta} \in [0, 1]^{n_v^s}$, and $\rho \in [0, 1]$, if $\bm{\theta} \leq \rho \bm{1}$, then $\mathbb{U}^s(v, \rho, \bm{\theta}) \subseteq \mathbb{U}^s$.

Figures (15)

  • Figure 1: Reach-avoid scenario where the ego vehicle (EV) aims at planning a safe trajectory in the presence of an uncertain surrounding vehicle (SV). (a) Deterministic approach: no consideration of motion uncertainty of the obstacle, therefore the planning is unsafe. (b) Worst-case robust approach: considering the worst-case motion uncertainty of the obstacle yields an infeasible problem. (c) The proposed approach: reducing the conservatism and planning a feasible reference trajectory.
  • Figure 2: Learning the set $\tilde{\mathbb{U}}_t^s$ by solving LP \ref{['LP:quanset']}.
  • Figure 3: The learned intended control sets by formulation \ref{['LP:quanset']}, formulation \ref{['LP:quansetonline']}, the moving-horizon (MH) method, and the rigid tube (RT) method (for the MH method $L = 30$ ). (a) The number of samples is $50$, $\mathbb{U}^s$ is a square. (b) The number of samples is $500$, $\mathbb{U}^s$ is a square. (c) The number of samples is $50$, $\mathbb{U}^s$ is a regular hexagon. (d) The number of samples is $500$, $\mathbb{U}^s$ is a regular hexagon. (e) The set volume with colors according to Fig. \ref{['fig: set with different samples']}(a). The dashed lines indicate the results with $\mathbb{U}^s$ as a regular hexagon, and solid lines indicate the results with $\mathbb{U}^s$ as a square.
  • Figure 4: Control actions of the system and volume of the learned set.
  • Figure 5: Learned control sets at different time steps (at $t=50$ the mild control behavior ends, and at $t=100$ the sampling ends). (a) With the online recursion formulation \ref{['LP:quansetonline']}. (b) With the MH approach.
  • ...and 10 more figures

Theorems & Definitions (11)

  • Remark 3.1
  • Example 3.1
  • Lemma 4.1
  • proof
  • Proposition 4.1
  • proof
  • Remark 4.1
  • Remark 4.2
  • Remark 4.3
  • Example 5.1
  • ...and 1 more