System and method for controlling motion of a vehicle in a stochastic disturbance field
The present disclosure discloses a system and method for controlling motion of a vehicle. The method comprises collecting a signal indicative of objectives of the motion and a value of the disturbances, and minimizing an objective function subject to constraints defined by the objectives of the motion to produce optimized values of parameters of a sequence of splines. The method further comprises controlling the motion of the vehicle based on a model of differentially flat dynamics of the vehicle according to an optimal path defined by the optimized values of the parameters of the sequence of splines.
1 . A control system for controlling motion of a vehicle, comprising:
a memory configured to store an objective function of the parameters defining a sequence of splines representing a path for the motion of the vehicle, wherein a first term of the objective function includes a total variation of the splines and their higher order derivatives, and wherein a second term of the objective function includes an energy function parameterized in the parameters of the sequence of splines and disturbances acting on the vehicle; and
a processor coupled with executable instructions that, when executed by the processor, cause the control system to:
collect a signal indicative of objectives of the motion and a value of the disturbances;
minimize the objective function subject to constraints defined by the objectives of the motion to produce optimized values of the parameters of the sequence of splines; and
control the motion of the vehicle based on a model of differentially flat dynamics of the vehicle according to an optimal path defined by the optimized values of the parameters of the sequence of splines.
2 . The control system of claim 1 , wherein the vehicle is one of an autonomous vehicle, a mobile robot, an aerial drone, a ground vehicles, an aerial vehicle, a water surface vehicle, or an underwater vehicle.
3 . The control system of claim 1 , wherein the motion of the vehicle is parameterized by the sequence of splines as parameterized curves, and wherein the parametrized curves include one or a combination of polynomials; Bezier curves; B-splines; truncated Fourier series; and Legendre polynomials.
4 . The control system of claim 1 , wherein the objective function is a weighted function of a minimum snap cost, a thrust cost, and a time cost, and wherein the minimum snap cost, the thrust cost, and the time cost are expressed in the parameters defining the sequence of splines.
5 . The control system of claim 1 , wherein the value of the disturbances is collected from one or a combination of meteorological forecasts, one or more sensors, Computer Fluid Dynamics (CFD) simulations with boundary conditions and a geometry of an environment in which the vehicle is controlled.
6 . The control system of claim 5 , wherein the processor is further configured to decompose the environment into sets of free space by computing a mesh.
7 . The control system of claim 6 , wherein the processor is further configured to:
assign measurements of the disturbances to the sets of free space; and
determine disturbance parameters based on the measurements assigned to the sets of free space.
8 . The control system of claim 7 , wherein the processor is further configured to collect new measurements of the disturbances and update the disturbance parameters based on the new measurements of the disturbances.
9 . The control system of claim 6 , wherein the processor is further configured to:
expand the sets of free space based on submodular optimization and greedy combination heuristics; and
determine the constraints based on the expanded sets of free space.
10 . The control system of claim 1 , wherein dynamics governing the vehicle motion satisfies a property of differential flatness.
11 . The control system of claim 1 , wherein the vehicle is an aerial vehicle, and the disturbance is modeled as wind and the energy function captures a change in thrust and/or torque caused by a movement of the vehicle in a field of the disturbance as a function of motion parameters.
12 . The control system of claim 1 , wherein the vehicle is a water surface vehicle, and the disturbance is modeled as wind and ocean currents, and the energy function captures a change in thrust and/or torque caused by a movement of the vehicle in a field of the disturbance as a function of motion parameters.
13 . The control system of claim 1 , wherein the vehicle is an underwater vehicle, and the disturbance is modeled as ocean currents, and the energy function captures a change in thrust and/or torque caused by a movement of the vehicle in a field of the disturbance as a function of motion parameters.
14 . A method for controlling motion of a vehicle, wherein the method uses a processor coupled to a memory storing an objective function of the parameters defining a sequence of splines representing a path for the motion of the vehicle, wherein a first term of the objective function includes a total variation of the splines and their higher order derivatives, and wherein a second term of the objective function includes an energy function parameterized in the parameters of the sequence of splines and disturbances acting on the vehicle, the processor is coupled with stored instructions that when executed by the processor carry out steps of the method, comprising:
collecting a signal indicative of objectives of the motion and a value of the disturbances;
minimizing the objective function subject to constraints defined by the objectives of the motion to produce optimized values of the parameters of the sequence of splines; and
controlling the motion of the vehicle based on a model of differentially flat dynamics of the vehicle according to an optimal path defined by the optimized values of the parameters of the sequence of splines.
15 . The method of claim 14 , wherein the vehicle is one of an autonomous vehicle, a mobile robot, an aerial drone, a ground vehicles, an aerial vehicle, a water surface vehicle, or an underwater vehicle.
16 . The method of claim 14 , wherein the motion of the vehicle is parameterized by the sequence of splines as parameterized curves, and wherein the parametrized curves include one or a combination of polynomials, Bezier curves, B-splines; truncated Fourier series, and Legendre polynomials.
17 . The method of claim 14 , wherein the objective function is a weighted function of a minimum snap cost, a thrust cost, and a time cost, and wherein the minimum snap cost, the thrust cost, and the time cost are expressed in the parameters defining the sequence of splines.
18 . The method of claim 14 , wherein the value of the disturbances is collected from one or a combination of meteorological forecasts, one or more sensors, Computer Fluid Dynamics (CFD) simulations with boundary conditions and a geometry of an environment in which the vehicle is controlled.
19 . The method of claim 18 , wherein the method further comprises:
decomposing the environment into sets of free space by computing a mesh;
assigning measurements of the disturbances to the sets of free space; and
determining disturbance parameters based on the measurements assigned to the sets of free space.
20 . A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, the storage medium stores an objective function of the parameters defining a sequence of splines representing a path for the motion of the vehicle, wherein a first term of the objective function includes a total variation of the splines and their higher order derivatives, and wherein a second term of the objective function includes an energy function parameterized in the parameters of the sequence of splines and disturbances acting on the vehicle, the program when executed by the processor carry out steps of the method, comprising:
collecting a signal indicative of objectives of the motion and a value of the disturbances;
minimizing the objective function subject to constraints defined by the objectives of the motion to produce optimized values of the parameters of the sequence of splines; and
controlling the motion of the vehicle based on a model of differentially flat dynamics of the vehicle according to an optimal path defined by the optimized values of the parameters of the sequence of splines.