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What is the model used in lqr_steer_control.py? #992
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Documentation for the LQR Steering Control Model Components: Control Inputs: Various parameters are used in the model, including the wheelbase L of the vehicle, the maximum steering angle max_steer, time step dt, and speed proportional gain Kp. The LQR controller is parameterized by the matrices Q and R, which define the cost function for the state and control inputs, respectively. State Space Representation: Define the state vector x comprising position, orientation, and velocity. Formulate the state transition equation x_next = A * x + B * u to represent the dynamics of the system. Linearize the state transition equation around the current state using Taylor series expansion. Convert the continuous-time state-space model to discrete-time by discretizing the dynamics using appropriate integration methods. Apply the LQR control design methodology to obtain the optimal control gain matrix K by solving the discrete-time Algebraic Riccati equation (DARE). Utilize the obtained matrices A, B, and K in the control algorithm to compute the optimal control input for the given state and desired trajectory. By following these steps, the linearized A, B matrix can be derived and integrated into the control algorithm to achieve effective trajectory tracking performance. |
@Gopigunaganti Thank you for great explanation!!. |
ok ! ,thanks for the reply . |
@Gopigunaganti Thanks for your full explanation of the control model !
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@lijieamd I have also encountered the same issue. Have you now understood the state-space equations for it? |
@AtsushiSakai Hello, I saw that you used the kinematics modeling of the vehicle in the LQR, and it seems that establishing the following equation for control can make the lateral error smaller (and I still don't understand how your current kinematic model is built):
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Let me explain it in the docs by PR #1015 |
Is there any documentation or related paper for this LQR lateral controller?
It seems like an error state model, but I don't know how to derive the linearized A,B matrix from scratch.
It would be great if there was some detailed explanation of the derivation steps.
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