DeepReach: A Deep Learning Approach to High-Dimensional Reachability

11/04/2020
by   Somil Bansal, et al.
0

Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical control systems. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the ability to deal with state and input constraints. However, it involves solving a PDE, whose computational and memory complexity scales exponentially with respect to the number of state variables, limiting its direct use to small-scale systems. We propose DeepReach, a method that leverages new developments in sinusoidal networks to develop a neural PDE solver for high-dimensional reachability problems. The computational requirements of DeepReach do not scale directly with the state dimension, but rather with the complexity of the underlying reachable tube. DeepReach achieves comparable results to the state-of-the-art reachability methods, does not require any explicit supervision for the PDE solution, can easily handle external disturbances, adversarial inputs, and system constraints, and also provides a safety controller for the system. We demonstrate DeepReach on a 9D multi-vehicle collision problem, and a 10D narrow passage problem, motivated by autonomous driving applications.

READ FULL TEXT
research
09/25/2022

Generating Formal Safety Assurances for High-Dimensional Reachability

Providing formal safety and performance guarantees for autonomous system...
research
12/07/2020

Real-Time Formal Verification of Autonomous Systems With An FPGA

Hamilton-Jacobi reachability analysis is a powerful technique used to ve...
research
10/14/2021

Safety-aware Policy Optimisation for Autonomous Racing

To be viable for safety-critical applications, such as autonomous drivin...
research
01/21/2022

Computation of Regions of Attraction for Hybrid Limit Cycles Using Reachability: An Application to Walking Robots

Contact-rich robotic systems, such as legged robots and manipulators, ar...
research
08/05/2021

Reachability-based Safe Planning for Multi-Vehicle Systems withMultiple Targets

Recently there have been a lot of interests in introducing UAVs for a wi...
research
04/04/2018

Numerical Verification of Affine Systems with up to a Billion Dimensions

Affine systems reachability is the basis of many verification methods. W...
research
10/15/2017

The Scaling Limit of High-Dimensional Online Independent Component Analysis

We analyze the dynamics of an online algorithm for independent component...

Please sign up or login with your details

Forgot password? Click here to reset