Attitude control system and method
Systems and method for controlling the attitude maneuvers of a spacecraft in space are provided. The method automatically generates optimal trajectories in real-time to guide a spacecraft, providing a much more robust and efficient method than predefined trajectories, to model errors or disturbances. These methods do not rely in predefined trajectories and their associated feed-forward term. The systems comprise sensors, attitude control mechanisms, and a control module to orient the spacecraft in real-time, such that the spacecraft reaches a desired target attitude following an optimal path in the state space and is locally and asymptotically stable.
1. An on-board attitude control system for controlling attitude maneuvers of a vehicle, the system comprising:
an attitude control mechanism operable to orient the vehicle; and
a control module configured to, at each step of multiple steps of a path:
determine, based at least in part on an attitude state estimated at each step of the multiple steps, and on a target attitude state, an attitude error;
determine, based at least in part on the attitude error, weighting factors of a cost function;
minimize the cost function to obtain a control action, wherein the cost function comprises a state error cost and a control effort cost; and
direct the attitude control mechanism to perform the control action to orient the vehicle,
wherein the weighting factors of the cost function are determined as a function of one or more zones of a state-space;
wherein minimizing the cost function comprises solving an Algebraic Riccati Equation (ARE) using a Newton-Rapshon method with a predetermined maximum number of iterations, starting with an initial guess chosen to yield a globally stabilizing solution of a closed loop system, wherein if no optimal solution is found for minimizing the cost function after the predetermined maximum number of iterations, an intermediate result is used to determine the control action, and the intermediate result is used as a next iteration initial guess of a first iteration of a next step.
2. The on-board attitude control system according to claim 1 , wherein the control action comprises torques to apply to the vehicle to orient the vehicle, and wherein the control module is further configured to minimize a sum of the norm of the torques along the path.
3. A satellite system comprising:
at least one sensor configured to estimate attitude states of the satellite system;
an on-board attitude control mechanism operable to orient the satellite system; and
an attitude control module configured to, at each step of multiple steps of a path:
determine, based at least in part on an attitude state estimated at each step of the multiple steps, and on a target attitude state, an attitude error, wherein the attitude state estimated at each step of the multiple steps is based at least in part on information from the at least one sensor;
determine, based at least in part on the attitude error, weighting factors of a cost function;
minimize the cost function to obtain a control action, wherein the cost function comprises a state error cost and a control effort cost; and
direct the on-board attitude control mechanism to perform the control action to orient the satellite system;
wherein the weighting factors of the cost function are determined as a function of one or more zones of a state-space;
wherein minimizing the cost function comprises solving an Algebraic Riccati Equation (ARE) using a Newton-Rapshon method with a predetermined maximum number of iterations, starting with an initial guess chosen to yield a globally stabilizing solution of a closed loop system, wherein if no optimal solution is found for minimizing the cost function after the predetermined maximum number of iterations, an intermediate result is used to determine the control action, and the intermediate result is used as a next iteration initial guess of a first iteration of a next step.
4. The satellite system according to claim 3 , wherein the control action comprises torques to apply to the satellite system to orient the satellite system, and wherein the attitude control module is further configured to minimize a sum of the norm of the torques along the path.
5. The satellite system according to claim 3 , wherein the at least one sensor is at least one of a gyroscope, a magnetometer, a star tracker, a horizon sensor, a sun sensor, or any combination thereof.
6. The satellite system according to claim 3 , wherein the on-board attitude control mechanism is at least one of a magnetorquer, a reaction wheel, a momentum wheel, a control momentum gyro, a thruster, or any combination thereof.
7. The satellite system according to claim 3 , wherein the target attitude state is determined based at least in part on a target orientation or a target orientation trajectory determined by an algorithm or a user, or based at least in part on a task the satellite system is tasked to perform.
8. A method for controlling attitude maneuvers of a vehicle, the method comprising, at each step of multiple steps of a path:
determining, based at least in part on an attitude state estimated at each step of the multiple steps, and on a target attitude state, an attitude error;
determining, based at least in part on the attitude error, weighting factors of a cost function;
minimizing the cost function to obtain a control action, wherein the cost function comprises a state error cost and a control effort cost; and
performing the control action to orient the vehicle;
wherein the method further comprises determining the weighting factors of the cost function as a function of one or more zones of a state-space;
wherein minimizing the cost function comprises solving an Algebraic Riccati Equation (ARE) using a Newton-Rapshon method with a predetermined maximum number of iterations, starting with an initial guess chosen to yield a globally stabilizing solution of a closed loop system, wherein if no optimal solution is found for minimizing the cost function after the predetermined maximum number of iterations, an intermediate result is used to determine the control action, and the intermediate result is used as a next iteration initial guess of a first iteration of a next step.
9. The method according to claim 8 , further comprising:
obtaining a mathematical expression representing kinematics and dynamics of a spacecraft system;
obtaining a pseudo-linearized expression of the mathematical expression; and
setting, based on the pseudo-linearized expression of the mathematical expression, the cost function.
10. The method according to claim 9 , wherein obtaining the pseudo-linearized expression of the mathematical expression comprises defining State-Dependent Coefficients (SDC), and the mathematical expression is based on Modified Rodrigues Parameters and Eulerian dynamic equations for a spacecraft with reaction wheels.
11. The method according to claim 8 , wherein the initial guess is chosen to be a positive definite matrix P 0 , with the following structure:
P
o
=
[
11
P
o
12
P
o
12
P
o
t
22
P
o
]
wherein 11 P 0 is a positive definite matrix and 12 P 0 and 22 P 0 are defined as follows:
(Π R ( x ) P gain ) t = 12 P o
Π R ( x ) D gain = 22 P o
wherein P gain and D gain are positive numbers, R(x) corresponds to the control effort cost of the cost function, Π=J−J z YY t is the grouped inertia, J∈R 3×3 is the inertia matrix of the vehicle written in Body frame, J z is the vehicle's reaction wheels' inertia along their spin vector, Y∈R 3×4 is the matrix which columns are the direction of each spin vector in Body versors.
12. The on-board attitude control system according to claim 1 , wherein the initial guess is chosen to be a positive definite matrix P 0 , with the following structure:
P
o
=
[
11
P
o
12
P
o
12
P
o
t
22
P
o
]
wherein 11 P 0 is a positive definite matrix and 12 P 0 and 22 P 0 are defined as follows:
(Π R ( x ) P gain ) t = 12 P o
Π R ( x ) D gain = 22 P o
wherein P gain and D gain are positive numbers, R(x) corresponds to the control effort cost of the cost function, Π=J−J z YY t is the grouped inertia, J∈R 3×3 is the inertia matrix of the vehicle written in Body frame, J z is the vehicle's reaction wheels' inertia along their spin vector, Y∈R 3×4 is the matrix which columns are the direction of each spin vector in Body versors.
13. The satellite system according to claim 3 , wherein the initial guess is chosen to be a positive definite matrix P 0 , with the following structure:
P
o
=
[
11
P
o
12
P
o
12
P
o
t
22
P
o
]
wherein 11 P 0 is a positive definite matrix and 12 P 0 and 22 P 0 are defined as follows:
(Π R ( x ) P gain ) t = 12 P o
Π R ( x ) D gain = 22 P o
wherein P gain and D gain are positive numbers, R(x) corresponds to the control effort cost of the cost function, Π=J−J z YY t is the grouped inertia, J∈R 3×3 is the inertia matrix of the vehicle written in Body frame, J z is the vehicle's reaction wheels' inertia along their spin vector, Y∈R 3×4 is the matrix which columns are the direction of each spin vector in Body versors.