Systems and methods for risk-bounded control barrier functions
System, methods, and other embodiments described herein relate to implementing risk-bounded control barrier functions. In one embodiment, a method includes estimating a state of a vehicle; planning a trajectory based on the state of the vehicle; determining a nominal control input based on the trajectory; applying a risk-bounded control barrier function to determine a control input; and applying the control input to the vehicle.
1 . A system, comprising:
a processor; and
a memory communicably coupled to the processor and storing machine-readable instructions that, when executed by the processor, cause the processor to:
estimate a state of a vehicle;
plan a trajectory based on the state of the vehicle;
determine a nominal control input based on the trajectory;
apply a risk-bounded control barrier function based on a Lipschitz continuous function a selected with respect to a stochastic analog generator and a function modifying an integral of the stochastic analog generator to determine a control input; and
execute the control input on the vehicle.
2 . The system of claim 1 , wherein the machine-readable instruction to plan the trajectory is further based on start-to-goal motion planning.
3 . The system of claim 2 , wherein the vehicle is a robotic or medical device.
4 . The system of claim 3 , wherein the state of the vehicle is at least one of a delivery rate, a filtering, or a titration rate.
5 . The system of claim 2 , wherein the state of the vehicle is at least one of a location, heading, or velocity.
6 . The system of claim 1 , wherein the machine-readable instruction to apply a risk-bounded control barrier function further includes modifying the integral of the stochastic analog generator based on a tolerable system risk parameter.
7 . The system of claim 6 , wherein the tolerable system risk parameter is bounded in relation to a Gauss error function.
8 . The system of claim 1 , wherein the machine-readable instruction to determine the nominal control input based on the trajectory is performed via automated driving assistance.
9 . A non-transitory computer-readable medium including instructions that when executed by one or more processors cause the one or more processors to:
estimate a state of a vehicle;
plan a trajectory based on the state of the vehicle;
determine a nominal control input based on the trajectory;
apply a risk-bounded control barrier function based on a Lipschitz continuous function α selected with respect to a stochastic analog generator and a function modifying an integral of the stochastic analog generator to determine a control input; and
execute the control input on the vehicle.
10 . The non-transitory computer-readable medium of claim 9 , wherein the instruction to plan the trajectory is further based on start-to-goal motion planning.
11 . The non-transitory computer-readable medium of claim 10 , wherein the state of the vehicle is at least one of a delivery rate, a filtering, or a titration rate.
12 . The non-transitory computer-readable medium of claim 10 , wherein the state of the vehicle is at least one of a location, heading, or velocity.
13 . The non-transitory computer-readable medium of claim 9 , wherein the instruction to apply a risk-bounded control barrier function further includes modifying the integral of the stochastic analog generator based on a tolerable system risk parameter.
14 . The non-transitory computer-readable medium of claim 13 , wherein the tolerable system risk parameter is bounded in relation to a Gauss error function.
15 . The non-transitory computer-readable medium of claim 9 , wherein the instruction to determine the nominal control input based on the trajectory is performed via automated driving assistance.
16 . A method, comprising:
estimating a state of a vehicle;
planning a trajectory based on the state of the vehicle;
determining a nominal control input based on the trajectory;
applying a risk-bounded control barrier function based on a Lipschitz continuous function a selected with respect to a stochastic analog generator and a function modifying an integral of the stochastic analog generator to determine a control input; and
executing the control input on the vehicle.
17 . The method of claim 16 , wherein planning the trajectory is further based on start-to-goal motion planning.
18 . The method of claim 16 , wherein applying a risk-bounded control barrier function further includes modifying the integral of the stochastic analog generator based on a tolerable system risk parameter.
19 . The method of claim 18 , wherein the tolerable system risk parameter is bounded in relation to a Gauss error function.
20 . The method of claim 16 , wherein determining the nominal control input based on the trajectory is performed via automated driving assistance.