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