In the context of optimal control for robotics, when dealing with a non-linear system, what is the primary motivation for employing linearization techniques, especially before applying methods like LQR?
Question 2
Consider a robotics task that requires a mobile robot to navigate an environment with dynamic obstacles. The control system must react quickly to avoid collisions while maintaining a desired path. Which characteristic of Model Predictive Control (MPC) makes it particularly advantageous for this type of problem?
Question 3
In an optimal control cost function, the weighting matrices (e.g., $Q$ and $R$ in LQR) play a crucial role. Which of the following best describes their primary function?
Question 4
In the context of optimal control, particularly with convex optimization problems often found in MPC formulations, what does the 'strong duality theorem' imply?
Question 5
When implementing a Linear Quadratic Regulator (LQR) for a robotic system, what is the primary challenge associated with accurately determining the state weighting matrix ($Q$) and the control weighting matrix ($R$)?
