Parameterized Fast and Safe Tracking (FaSTrack) using Deepreach

TL;DR

The paper tackles the challenge of providing safety guarantees for real-time autonomous navigation in unknown environments, where traditional HJ reachability is computationally prohibitive. It proposes Parametric FaSTrack (PF), a framework that couples DeepReach's parametric value-function learning with FaSTrack's safety guarantees to adapt online via a planner control bound $eta$. PF offline-trains a parameterized value function $V_ heta(r,t;eta)$, yielding static and dynamic tracking error bounds ($sTEB$ and $dTEB$) and a tracking controller, and online adapts $eta$ based on obstacle proximity to trade safety for speed. Experiments on a 6D Dubin's car and a 13D quadcopter demonstrate that PF can achieve substantial speedups (up to ~40%) while maintaining safety, highlighting the method's scalability to high-dimensional systems and its practical impact for safe, fast autonomous planning.

Abstract

Fast and Safe Tracking (FaSTrack) is a modular framework that provides safety guarantees while planning and executing trajectories in real time via value functions of Hamilton-Jacobi (HJ) reachability. These value functions are computed through dynamic programming, which is notorious for being computationally inefficient. Moreover, the resulting trajectory does not adapt online to the environment, such as sudden disturbances or obstacles. DeepReach is a scalable deep learning method to HJ reachability that allows parameterization of states, which opens up possibilities for online adaptation to various controls and disturbances. In this paper, we propose Parametric FaSTrack, which uses DeepReach to approximate a value function that parameterizes the control bounds of the planning model. The new framework can smoothly trade off between the navigation speed and the tracking error (therefore maneuverability) while guaranteeing obstacle avoidance in a priori unknown environments. We demonstrate our method through two examples and a benchmark comparison with existing methods, showing the safety, efficiency, and faster solution times of the framework.

Figures (6)

• Figure 1: Left figure denotes the offline framework (performed once), and the right figure denotes the online framework (performed every iteration). Components of FaSTrack are shown in blue, while components of PF are shown in orange.
• Figure 2: (Left) TEB for system \ref{['eqn: para Dubins']} with different planner control bounds $\beta$. Training parameters: 40k pre-train iterations, followed by 110k training iterations. The model is trained until convergence. Total training took 10h32m on a NVIDIA A30. As $\beta$ increases, the TEB grows larger. (Right) comparison between standard dynamic programming based HJ reachability (using codebase HelperOC) and DeepReach. Empirically, DeepReach produces more conservative error bounds.
• Figure 3: Online simulation of 6D Dubin's car. The trajectory is color-coded with the speed of planning: low $\beta = 0.5$ (blue), medium $0.5 < \beta \leq 1$ (purple), and high $\beta > 1$ (red). The goal (green dot) and current tracker state (red dot) are shown. The sTEB is in green. The dTEB for the current $\beta$ is in orange. The dotted circle around the tracker represents the sensing range. The left panel shows the planner applying $\beta_u$ at the initial time since no obstacles are sensed. In the second panel, the system senses an obstacle ($\mathcal{K} \subseteq \mathcal{B}_{e,s}^\infty$), and slows down to reduce the corresponding TEB. In the third panel, the system applies higher $\beta$ values as it moves away from the obstacles and towards the goal.
• Figure 4: Tracker moving away from the obstacle. $\mathcal{K}$ expands and safety is preserved.
• Figure 5: Trajectory for F, MF PF, and MPPI. Trajectory colors correspond to Fig. \ref{['fig:3']}. MPPI does not have a color since it does not have a $\beta$.

Theorems & Definitions (1)

• Remark 1