FaSTrack: a Modular Framework for Fast and Guaranteed Safe Motion Planning (1703.07373v2)

Abstract: Fast and safe navigation of dynamical systems through a priori unknown cluttered environments is vital to many applications of autonomous systems. However, trajectory planning for autonomous systems is computationally intensive, often requiring simplified dynamics that sacrifice safety and dynamic feasibility in order to plan efficiently. Conversely, safe trajectories can be computed using more sophisticated dynamic models, but this is typically too slow to be used for real-time planning. We propose a new algorithm FaSTrack: Fast and Safe Tracking for High Dimensional systems. A path or trajectory planner using simplified dynamics to plan quickly can be incorporated into the FaSTrack framework, which provides a safety controller for the vehicle along with a guaranteed tracking error bound. This bound captures all possible deviations due to high dimensional dynamics and external disturbances. Note that FaSTrack is modular and can be used with most current path or trajectory planners. We demonstrate this framework using a 10D nonlinear quadrotor model tracking a 3D path obtained from an RRT planner.

• The paper presents the FaSTrack algorithm that decouples planning and tracking to achieve rapid motion planning with guaranteed safety.
• It employs Hamilton-Jacobi reachability analysis to precompute a tracking error bound that maintains safe operation in the presence of disturbances.
• Empirical results from a 10-dimensional quadrotor study demonstrate effective navigation in cluttered, dynamically changing environments.

Overview of FaSTrack: A Modular Framework for Fast and Guaranteed Safe Motion Planning

The paper "FaSTrack: A Modular Framework for Fast and Guaranteed Safe Motion Planning" presents a novel approach to addressing some pressing challenges in the domain of motion planning for autonomous systems. The research aims to balance the need for rapid planning with guarantees of safety and dynamic feasibility, advancing the conversation on efficient and safe navigation of high-dimensional dynamical systems in environments that are a priori unknown.

Primary Contributions and Methodology

The primary contribution of this work is the introduction of the FaSTrack algorithm, which decouples the motion planning problem into two components: a simplified planning model and a sophisticated tracking model. The planning model utilizes simplified dynamics for efficient real-time path or trajectory planning, whereas the tracking model accounts for the full range of system dynamics as well as external disturbances. This separation provides a framework to guarantee safety without the computational cost usually associated with high-dimensional dynamic systems.

The FaSTrack algorithm employs a pre-computation phase involving Hamilton-Jacobi (HJ) reachability analysis to derive a tracking error bound. This bound quantifies the maximum possible deviation between the paths computed by the simplified planning model and the actual trajectories followed by the tracking model, considering all potential external disturbances. The offline computation of these bounds, expressed as a "safety bubble," allows the real-time system to operate efficiently by utilizing a precomputed look-up table for optimal control decisions.

Results and Demonstration

The framework was demonstrated through a high-dimensional case paper involving a 10-dimensional quadrotor model tracking a path generated by a rapidly-exploring random tree (RRT) planner. The results provide empirical evidence supporting the method's capability to maintain trajectories within safe bounds while traversing through cluttered environments affected by disturbances such as wind. The quadrotor successfully navigated these environments, illustrating that it could incorporate real-time trajectory adjustments to maintain safety without compromising performance.

Theoretical and Practical Implications

The theoretical bearings of this work lie in its innovative application of differential games and HJ reachability to establish theoretically sound safety guarantees. By effectively creating a dynamic interplay between planning and tracking systems, FaSTrack demonstrates how complex systems can maintain safe operation by preemptively accounting for worst-case perturbations.

Practically, FaSTrack offers a pathway to integrate sophisticated dynamic models into the real-time operation of UAVs and other autonomous vehicles without incurring typical computational inefficiencies. This research enhances the prospects for deploying autonomous systems in dynamic and unpredictable environments where rapid re-planning is vital, thus extending the applicability of autonomous systems in real-world scenarios.

Future Directions

The exploration of FaSTrack opens several avenues for future research. One potential development could involve extending the framework to dynamically evolving environments where obstacles are not static. Another area of interest includes the modification of the tracking error bounds in response to real-time assessments of external disturbances, further enhancing adaptability and robustness. Additionally, the applicability of FaSTrack with various types of real-time planners beyond RRT, such as model predictive control (MPC) and learning-based methods, represents a promising direction to pursue.

In conclusion, the FaSTrack framework offers significant strides toward bridging the dichotomy between speed and safety in autonomous navigation, promising broader adoption in advanced robotics applications that demand high efficiency without compromising safety.