Output- and State-Dependent Riccati Equation: Space Robotics

These files present output- and state-dependent Riccati equation (OSDRE) for general differential equations and free-floating space robot.

The codes for output- and state-dependent Riccati equation (OSDRE) are presented for a set of coupled k-th order ordinary differential equations (ODEs).

Use “Run_Section_4_1_A_y_derivation” for derivation of the outputs and “Run_Section_4_1_B_Simulation_Math_Model” for the simulation.

The output feedback design removes outer layers of kinematics or coordinate transformations in some systems and directly controls the output dynamics. This enables efficient control over many systems in which there is an indirect relation between outputs and states such as robots, mobile manipulators, autonomous vehicles, unmanned aerial vehicles, etc. The application of the OSDRE is devoted to the control of free-floating space manipulators (FFSM). The end-effector position of the FFSM is a function of mobile base coordinates (position and orientation) that are not actuated due to the free-floating condition. Then the output feedback SDRE directly controls the end-effector and guides the mobile base to provide enough reaction force/moment to push the gripper towards the desired end-point. Simulation codes for a three-link FFSM are also reported in:

Basic code, three-link: “Run_Section_4_2_03_3Links_Mobile_Base_Output_Feedback”

Workspace analysis, three-link: “Run_Section_4_2_04_3Links_Mobile_Base_Output_Feedback_Workspace”

Comparison, three-link: “Run_Section_4_2_05_3Links_Mobile_Base_Output_Feedback_Comp”

Two-link robot: “Run_Section_4_2_06_2_Links_Mobile_Base_Output_Feedback”

Three-link with end-effector pose: “Run_Section_4_3_02_3Links_Mobile_Base_Output_Feedback_plot”

The details, formulations, and more information could be found in the following article:

Nekoo, S. R. (2022). Output-and State-Dependent Riccati Equation: An Output Feedback Controller Design. Aerospace Science and Technology, 107649. https://doi.org/10.1016/j.ast.2022.107649

The notation in the codes are based on the above report, and videos of the simulations could be seen on the journal website.