Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Autonomy Architectures for Safe Planning in Unknown Environments Under Budget Constraints

Daniel M. Cherenson, Devansh R. Agrawal, Dimitra Panagou

TL;DR

This work tackles online planning for nonlinear systems in unknown environments under budget constraints by formulating a gatekeeper framework paired with a novel backup-trajectory generator, ReRoot. ReRoot builds a reverse-rooted forest of dynamically feasible backups rooted at budget-renewal sets and selects low-cost backups to steer the nominal plan toward renewal regions, thereby guaranteeing safety and budget satisfaction for all time. The authors prove recursive feasibility within the gatekeeper and demonstrate the approach on a GNSS-denied UAV with visual odometry, showing the system maintains safety and keeps the localization error budget within bounds while progressing toward a goal. The method enables principled backup control in uncertain environments and provides a practical, online solution for safety-critical planning with renewable resources.

Abstract

Mission planning can often be formulated as a constrained control problem under multiple path constraints (i.e., safety constraints) and budget constraints (i.e., resource expenditure constraints). In a priori unknown environments, verifying that an offline solution will satisfy the constraints for all time can be difficult, if not impossible. We present ReRoot, a novel sampling-based framework that enforces safety and budget constraints for nonlinear systems in unknown environments. The main idea is that ReRoot grows multiple reverse RRT* trees online, starting from renewal sets, i.e., sets where the budget constraints are renewed. The dynamically feasible backup trajectories guarantee safety and reduce resource expenditure, which provides a principled backup policy when integrated into the gatekeeper safety verification architecture. We demonstrate our approach in simulation with a fixed-wing UAV in a GNSS-denied environment with a budget constraint on localization error that can be renewed at visual landmarks.

Autonomy Architectures for Safe Planning in Unknown Environments Under Budget Constraints

TL;DR

This work tackles online planning for nonlinear systems in unknown environments under budget constraints by formulating a gatekeeper framework paired with a novel backup-trajectory generator, ReRoot. ReRoot builds a reverse-rooted forest of dynamically feasible backups rooted at budget-renewal sets and selects low-cost backups to steer the nominal plan toward renewal regions, thereby guaranteeing safety and budget satisfaction for all time. The authors prove recursive feasibility within the gatekeeper and demonstrate the approach on a GNSS-denied UAV with visual odometry, showing the system maintains safety and keeps the localization error budget within bounds while progressing toward a goal. The method enables principled backup control in uncertain environments and provides a practical, online solution for safety-critical planning with renewable resources.

Abstract

Mission planning can often be formulated as a constrained control problem under multiple path constraints (i.e., safety constraints) and budget constraints (i.e., resource expenditure constraints). In a priori unknown environments, verifying that an offline solution will satisfy the constraints for all time can be difficult, if not impossible. We present ReRoot, a novel sampling-based framework that enforces safety and budget constraints for nonlinear systems in unknown environments. The main idea is that ReRoot grows multiple reverse RRT* trees online, starting from renewal sets, i.e., sets where the budget constraints are renewed. The dynamically feasible backup trajectories guarantee safety and reduce resource expenditure, which provides a principled backup policy when integrated into the gatekeeper safety verification architecture. We demonstrate our approach in simulation with a fixed-wing UAV in a GNSS-denied environment with a budget constraint on localization error that can be renewed at visual landmarks.

Paper Structure

This paper contains 10 sections, 1 theorem, 31 equations, 5 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Method Overview
  4. Guaranteed Constraint Satisfaction
  5. ReRoot for Backup Trajectory Construction
  6. Backup Trajectory Generation Problem
  7. ReRoot (Reverse Rooted Forest)
  8. Backup Trajectory Generation
  9. Simulation Case Study
  10. Conclusion

Key Result

Theorem 1

Suppose $p_0^{\textup{can},T_S}$ is a dynamically feasible candidate trajectory defined on $[t_0,\infty)$ that is valid by Def. def:valid for some $T_S\ge0$. If $p_k^{\textup{com}}$ is determined via Def. def:com, then

Figures (5)

  • Figure 1: Block diagram of our proposed layered autonomy architecture, with our module gatekeeper + ReRoot highlighted in the dashed line.
  • Figure 2: Snapshots of gatekeeper with ReRoot trees rooted at budget renewal sets. The trees are grown in the free set $\mathcal{F}_k$. The robot discovers new budget renewal sets as it uncovers more of the unknown space.
  • Figure 3: Top-down view of field environment from the VPAIR database schleiss2022vpair. The white dots are visual odometry features. Note the lack of features in certain areas. The orange circle is the starting location. The yellow circle is the goal location. The white circle is a landmark. The nominal trajectory in black is the path of minimum distance, which becomes unsafe at the red "!". The magenta line is the omniscient trajectory, i.e., has knowledge of all feature locations, that minimizes distance while satisfying the safety and budget constraints.
  • Figure 4: (a)-(d) Visualization of the simulated experiment of gatekeeper with ReRoot at various times in the mission. The features seen by the UAV are the white dots. The orange dot is the starting location, the gray dot is a landmark, and the yellow dot is the goal location. The colored thin lines are the branches of the ReRoot forest. The blue line is the UAV's path up to time $t$. The black line is the unsafe part of the nominal trajectory, and the red line is the nominal component of the committed trajectory, which is replanned from the UAV position when the committed trajectory deviates from the nominal. The green line is the backup component of the committed trajectory and reaches a budget renewal set. (e) Value of the budget state $b$ (absolute position error) over time, which resets whenever the UAV reaches a budget renewal set. The budget never exceeds the maximum allowed value of 9 m. (f) Number of features in the FOV over time, which is never below the minimum $N_f = 8$. The gray refers to when the UAV is at a landmark.
  • Figure 5: (a) Simulation result of the same setup as in \ref{['fig:simulation']} but with a budget constraint of 5 m of localization error. (b) Despite never reaching the goal, the budget constraint is always satisfied and (c) the safety constraint is also always satisfied. A limit cycle-like behavior is observed, illustrating that gatekeeper can successfully prevent the robot from leaving the safe set when the mission cannot be executed safely.

Theorems & Definitions (11)

  • Definition 1: Controlled Invariant Set
  • Definition 2: Backup Set
  • Definition 3: Trajectory
  • Definition 4: Nominal Trajectory
  • Definition 5: Backup Trajectory
  • Definition 6: Candidate Trajectory
  • Definition 7: Valid Trajectory
  • Definition 8: Committed Trajectory
  • Theorem 1
  • proof
  • ...and 1 more