Computer-implemented method and system for providing safe control inputs u(k) for actuator components of a vehicle

A computer-implemented method for providing safe control inputs u(k) for actuator components of a vehicle for implementing a specified trajectory, the method comprising the following steps:

• a. determining a vehicle state x(k) at a first time k;
• b. providing a first set of control inputs uper(k) for the first time k;
• and
• c. checking whether the first set of control inputs uper(k) is safe by checking whether a vehicle state x(k+1) for a later second time k+1 predicted based on the vehicle state x(k) and the first set of control inputs uper(k) is safe;
• wherein the predicted vehicle state x(k+1) is considered safe when the predicted vehicle state x(k+1) is within a predetermined maximum controlled invariant (MCI) state set C∞, and,
• when the vehicle state x(k+1) is not considered safe, a safe set of control inputs u(k) is determined by modifying the first set of control inputs uper(k) such that a vehicle state x(k+1) predicted based on the vehicle state x(k) and the modified set of control inputs u(k) is considered safe;
• wherein the MCI state set C∞ is described as
• C
• ∞
• =
• Δ
• {
• x
• ∈
• R
• n
• |
• h
• ⁡
• (
• x
• )
• ≤
• 0
• }
• ,
• where h(x(k))≤0 describes a condition that C∞ includes all permissible vehicle states x(k)∈X for which a set of control inputs u(k)∈U exists which transfers the vehicle into a safe state for a next time k+1, for all possible sets of disruptive influences w(k)∈W;
• and
• wherein, when checking whether the predicted vehicle state x(k+1) is safe, it is checked whether the condition:
• h
• ⁡
• (
• f
• ⁡
• (
• x
• ⁡
• (
• k
• )
• ,
• u
• per
• (
• k
• )
• ,
• w
• ⁡
• (
• k
• )
• )
• )
• ≤
• (
• 1
• -
• γ
• )
• ⁢
• h
• ⁡
• (
• x
• ⁡
• (
• k
• )
• )
• is fulfilled for all possible sets of disruptive influences w(k)∈W,
• where γ is a specifiable value greater than 0 and less than/equal to 1, γ∈(0, 1].