[Paper Review] Safe Sequential Path Planning of Multi-Vehicle Systems Under Presence of Disturbances and Imperfect Information.

Somil Bansal, Mo Chen+2 more|arXiv (Cornell University)|Mar 16, 2016

Robotic Path Planning Algorithms8 references13 citations

TL;DR

This paper extends sequential path planning (SPP) for multi-UAV systems to handle disturbances and imperfect information about higher-priority vehicles, using three robust methods that maintain linear computational complexity. It enables safety guarantees in realistic, uncertain environments where prior SPP methods assumed perfect knowledge and no disturbances.

ABSTRACT

Recently, there has been an immense surge of interest in using unmanned aerial vehicles (UAVs) for civil purposes. Multi-UAV systems are safety-critical, and safety guarantees must be made to ensure no undesirable configurations such as collisions occur. Hamilton-Jacobi (HJ) reachability is ideal for analyzing such safety-critical systems because it provides safety guarantees and is flexible in terms of system dynamics; however, its direct application is limited to small-scale systems of no more than two vehicles because of the exponential-scaling computation complexity. By assigning vehicle priorities, the sequential path planning (SPP) method allows multi-vehicle path planning to be done with a computation complexity that scales linearly with the number of vehicles. Previously the SPP method assumed no disturbances in the vehicle dynamics, and that every vehicle has perfect knowledge of the position of higher-priority vehicles. In this paper, we make SPP more practical by providing three different methods for accounting for disturbances in dynamics and imperfect knowledge of higher-priority vehicles. Each method has advantages and disadvantages with different assumptions about information sharing. We demonstrate our proposed methods in simulations.

Motivation & Objective

• Address the limitation of prior SPP methods that assume no disturbances and perfect knowledge of higher-priority vehicles.
• Enable safe path planning in real-world scenarios where vehicle dynamics are affected by disturbances and position information is uncertain.
• Maintain the linear computational complexity of SPP while incorporating uncertainty and disturbances.
• Provide multiple robust methods tailored to different assumptions about information sharing and system uncertainty.
• Demonstrate the practicality of SPP in complex, safety-critical multi-vehicle operations under realistic conditions.

Proposed method

• Adapt Hamilton-Jacobi (HJ) reachability analysis to account for process disturbances in vehicle dynamics by incorporating bounded uncertainty sets.
• Introduce three distinct methods to handle imperfect knowledge of higher-priority vehicles: conservative estimation, interval-based prediction, and robust reachability set propagation.
• Use prioritized sequential planning where each vehicle plans its path based on the predicted reachable sets of higher-priority vehicles.
• Maintain linear scaling with the number of vehicles by avoiding full simultaneous reachability computation.
• Model disturbances as bounded additive noise in the system dynamics to preserve safety guarantees.
• Apply reachability analysis to compute backward reachable sets that ensure collision avoidance under uncertainty.

Experimental results

Research questions

• RQ1 How can sequential path planning be extended to handle bounded process disturbances in multi-vehicle UAV systems?
• RQ2 What are the trade-offs between different strategies for handling imperfect knowledge of higher-priority vehicle positions?
• RQ3 Can safety guarantees be preserved under uncertainty while maintaining linear computational complexity?
• RQ4 How do varying assumptions about information sharing affect the robustness and conservativeness of the path planning solution?

Key findings

• The proposed methods successfully extend SPP to systems with bounded disturbances and imperfect information, maintaining safety guarantees.
• Three distinct approaches were developed, each suitable for different assumptions about uncertainty and information sharing.
• The computational complexity remains linear with respect to the number of vehicles, preserving scalability.
• Simulations demonstrate that the methods prevent collisions even under dynamic disturbances and position uncertainty.
• The conservative estimation method provides the tightest safety margins but with higher path conservativeness.
• The interval-based prediction method offers a balance between safety and path efficiency under partial information.