Safety Potential (SP)#
Description#
The SP is a part of the Safety Force Field (SFF) framework, which proposes a method to compute safe control policies on a collision-avoidance level. Conceptually, the SFF tries to identify, under the assumption of all actors conducting some safe control policy (e.g. an emergency brake), whether there can exist a conflict [Nister2019]. To measure how unsafe w.r.t to collision avoidance a situation is, SFF uses SP as a numeric valuation.
SFF assumes that each actor \(A_1 \in \mathcal{A}\) has a set of safe control policies, \(S_1\). Each safe control policy \(s \in S_1\) brings an actor \(A_1\) to a full stop in finite time. SFF defines the occupied set \(O_1\) of an actor \(A_1\) to include its safety margin as well as \(A_1\) itself. For each point on each trajectory that can arise from conducting a safe control policy \(s \in S_1\), \(O_1\) is examined. The resulting union of trajectories is the claimed set \(C_1\).
The unsafe set between two actors \(A_1, A_2 \in \mathcal{A}\) can then be identified as \(U_{1,2} = \{ x \in C_1 \times C_2 \mid C_1(x) \cap C_2(x) \neq \emptyset \}\). Intuitively, it is the set of all actor state combinations for which there exist safe control policies leading to a collision.
Identifying the combined state space of \(A_1\) and \(A_2\) as \(\Omega_1 \times \Omega_2\), SFF subsequently employs a potential function \(\rho_{1,2}: \Omega_1 \times \Omega_2 \to \mathbb{R}\) to rate the combined states of actors, where
\(\rho_{1,2}(u) > 0\) for all \(u \in U_{1,2}\) and
\(\rho_{1,2}(u) \geq 0\) for all \(u \not\in U_{1,2}\) and
\(\rho_{1,2}(x) \geq \rho_{1,2}(x')\) if \(x'\) is a state derived from \(x\) by \(A_1, A_2\) applying \(s_1, s_2 \in S_1, S_2\).
The safety potential can hence rate a two-actor scene from one of their perspectives.
The authors state the following exemplary safety potential for some \(k \in \mathbb{Z}_{>0} \cup \{\infty\}\):
where \(t_{int}\) is the the earliest intersection time when continuing the current situation under some model, and \(t_\mathit{stop}(A_i)\) is the time of full stop of \(A_i\) after applying a safety procedure.
Note that this framework can be extended with various more complex safety potentials [Nister2019]. Downstream, SFF uses the gradient of the safety potential to optimize for a safe control policy, if necessary.
Properties#
Run-time capability#
Yes
Target values#
No
Subject type#
Automated road vehicles
Scenario type#
Any for whose entities corresponding safety potentials and procedures can be defined
Inputs#
For \(k\) actors: states (e.g. \(p_i\), \(d_i\), \(v_i\)), safety procedures \(S_i\) and definition of safety potential \(\rho_{i,j}\) for \(i,j \in \{1, \dots, k\}\)
Output scale#
\([0, \infty)\), number, ordinal scale
Reliability#
High, but additionally depends on the reliability of the safety potentials
Validity#
High inside time window, but greatly dependent on validity of potential definition; no empirical analysis available
Sensitivity#
Potentially high, but depends on safety procedures and potential definition
Specificity#
Potentially high, but depends on safety procedures and potential definition
Prediction model#
Time window#
Duration of safety procedure
Time mode#
Branching time