An Efficient Reachability-Based Framework for Provably Safe
Autonomous Navigation in Unknown Environments
This paper investigates the problem of safe control in an a priori unknown environment. Since
the unknown parts of the environment can include unsafe regions, these regions are needed to
be treated as unsafe until otherwise observed in order to ensure safety. However, updating the
safe regions in real time is needed to avoid over-conservatism and causing sub-optimal policies.
This paper proposes a Hamilton-Jacobi reachability analysis based approach that can guarantee
safety for systems with nonlinear dynamics and disturbances under the assumption of perfect
sensors (within their ranges). The proposed method gives an optimal controller in addition to
the safe input set that is controllable under worst-case disturbances.
The approach of this paper is two-fold: First part is to compute backward reachable sets (BRS)
for the given unsafe region where BRS means the set of states that can lead to the given unsafe
region despite best control. And the second part is to update the unsafe regions regularly in
order to get smaller BRSs which translates to less conservative safe sets. This paper proposes
two new techniques that can be used to compute BRSs faster which allow them to run their
algorithm in real-time. After introducing their algorithm and these novel techniques, they
showcase their performance in different settings where different sensors (camera and lidar
based) and different planners (sampling based and model based). They also have an hardware
demonstration with a learning-based planner.
The main strength of the paper is its generality. The proposed techniques can be used in many
different settings. Moreover, their experimental results explain how their BRS computation
techniques impact the computation time and conservatism. Also, the paper discussed practical
considerations like numerical errors which improve its applicability in real-life.
The main weakness of the paper is that it is not possible to get a good sense of how much their
method interfere with the optimal control. I believe this should be studied further. Also, as
noted in the paper, noisy sensors are an interesting direction that should be investigated.
Alperen Tercan