You’re in your vehicle driving on the highway. While you round a large part, the thing is a deer in the center of the road. Are you in a position to slam in your brakes and decelerate before you decide to hit the deer? Otherwise, are you in a position to swerve taken care of securely? When are you currently condemned to crash? Could we make control systems in cars that ensure you’ll never be ready where you stand condemned to crash?

Safety analysis uses tools like Hamilton-Jacobi Reachability to obtain the mathematical solutions to such questions. Your house I’ve some system that evolves with time (e.g. a vehicle, a glucose monitor, an Heating and cooling system inside a house) and I’m also able to define what can be unsafe for your system (e.g. hitting obstacles, allowing glucose to decrease to harmful levels, letting a home get too warm or freezing). Safety analysis claims to obtain the group of initial conditions that the body will in the end enter individuals unsafe conditions (e.g. when you’re in a vehicle at high speeds headed straight to have an obstacle, and regardless of how hard you brake or turn you’re going too quickly to avoid an accident). Knowing this reachable set of initial conditions that cause unsafe states, you are able to work to make sure that your systems won’t ever enter individuals inevitable conditions.

What’s Hamilton-Jacobi (HJ) Reachability Analysis?

The Brief Explanation

HJ reachability analysis is about optimal control and guarantees for reaching goals and remaining safe. When given an engaged system along with a goal, this process creates the group of initial states that the body is certain to achieve that goal when utilizing optimal control. In addition to this, the technique offers the optimal control to achieve the aim. This may also be accomplished for obstacles and unsafe states: HJ reachability will give you some initial claims that the body must avoid to be able to remain safe, along with the control to achieve this. We are able to combine scenarios with goals and obstacles, so we may even consider worst-situation disturbances (e.g. wind).

The Thorough Explanation

Please visit our tutorial paper for any more thorough introduction.

Available Toolboxes

helperOC (MATLAB) — Our public code for computing reachable sets could be cloned or downloaded at https://github.com/HJReachability/helperOC (note: this really is basically a person-friendly wrapper with extra functionality for Prof. Ian Mitchel’s level set toolbox). This MATLAB repository is easily the most user-friendly, as well as contains lots of visualization functionality. However that it’s less efficient because the other toolboxes.

BEACLS (C++) — BEACLS means Berkeley Efficient API in C++ for Level Set methods. It’s basically a reimplementation from the MATLAB toolboxes in C++ with tweaks to enhance efficiency and compatibility with GPUs. It is extremely a little quicker than the MATLAB implementation, but sacrifices readability for performance.

enhanced_dp (Python/C++) — This toolbox was built by Prof. Mo Chen, with the aim of getting a simple python-based interface to setup a reachability problem, after which conversion to fast C++ code via HeteroCL.

Why Study HJ Reachability?

Reachability analysis is very helpful in complete safety-critical scenarios. When flying an airplane or administering anesthetics, accidental mistakes from less rigorous planning methods can lead to disaster. Reachability has the capacity to provide guarantees on which is protected, in addition to how you can implement controls to complete your ultimate goal. In addition to this, HJ Reachability are designed for nonlinear dynamics and worst-situation exterior disturbances.

The difficulties in HJ reachability lie in the costly computational cost. Because of the nature of dynamic programming the computational complexity of solving a reachability problem increases tremendously with the amount of dimensions within the system. Which means that systems using more than ~4 dimension is generally intractable to resolve analyses for. We’ve been focusing on techniques to circumvent this problem by splitting software in separate sub-systems that may be solved individually after which recombined. With respect to the system and also the decomposition we are able to acquire either exact or conservative outcomes of the real reachable set or tube. Find out more on the decomposition workhere.

Another fun research direction would be to merge the guarantees of reachability using the speed and ease of other path planning methods. An example may be the framework FaSTrack: Fast and Safe Tracking. In this project we created a tool to precompute an optimum tracking error bound from a easy and an elaborate type of an autonomous system. This enables us to organize trajectories with an atmosphere while using simple model, while making certain an optimum bound around the tracking error between this planned trajectory and also the performed trajectory. More info on FaSTrack are available here.

Finally, we’re always searching for interesting and new applying reachability. Our core application area continues to be both manned aerial systems and UAVs, however with the current advances we’ve produced in theory we could expand our achieve in applications for example biological systems, ecological systems, and power systems.