FaSTrack:A Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking

Abstract

Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replanning and guaranteed safety. In this framework, real-time computation is achieved by allowing any trajectory planner to use a simplified planning model of the system. The plan is tracked by the system, represented by a more realistic, higher-dimensional tracking model. We precompute the tracking error bound (TEB) due to mismatch between the two models and due to external disturbances. We also obtain the corresponding tracking controller used to stay within the TEB. The precomputation does not require prior knowledge of the environment. We demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and three different real-time trajectory planners with three different tracking-planning model pairs.

Robust Control Barrier-Value Functions for Safety-Critical Control

“…Therefore, such optimal control policy is often too restrictive to be used as a safety filter for a reference control signal. In the reachability community, to remedy this, a common practice is to switch from the reference control to the safe optimal control only when V (x(s), s) is close to 0, so called least-restrictive control law [17], [22], [23]. The resulting control system with such switching law may give undesirable jerky behaviors and is prone to errors in numerically computed D x V .…”

Learning Safe, Generalizable Perception-based Hybrid Control with Certificates

“…1, and it must navigate to a goal point while avoiding collisions. In contrast with higher-level approaches that combine SLAM with a global path planner, or robust planning approaches like [16], we restrict our focus to real-time controllers with feedback from local observations. Our observation-feedback controller can be combined with SLAM and planning modules to track waypoints along a path, but it can also be used without those components, or when those components fail, without compromising safety.…”

Ellipsotopes: Combining Ellipsoids and Zonotopes for Reachability Analysis and Fault Detection

“…Such a function can be approximated on a grid [29], [30] or as a polynomial [31]. Level sets can be used to conservatively compute reachable sets of robots and similar systems subject to uncertainty [1], [4], [32], [33]. In the special case of rigidbody robot motion planning with polynomial level sets, one can represent collision checking as a polynomial evaluation [1]; however, in general, Minkowski sums, intersections, and convex hulls can be approximated using sums-of-squares programming.…”

“…In the controls, robotics, and navigation communities, it is often critical to place strict guarantees on the behavior of a dynamical system. Example applications of such guarantees include collision avoidance [1]- [4], fault detection [5], [6], and control invariance [4], [7], [8]. A common strategy for enforcing such guarantees, especially for uncertain dynamical systems, is to compute the system's reachable set of states, then guarantee that this set lies within certain bounds (e.g., for fault detection) or obeys non-intersection constraints (e.g., for collision avoidance).…”