an MPC (Model Predictive Control) problem formulation, where the goal is to drive the center of mass (CoM) of a robot to a desired reference position while ensuring it stays within a support polygon and satisfies various constraints (such as position, velocity, and acceleration). Let's break down the terms and the optimization problem. Objective Function: The optimization problem minimizes an objective function that includes: State tracking error : ∑ k = 0 N − 1 ( x k − r k ) T Q ( x k − r k ) \sum_{k=0}^{N-1} (x_k - r_k)^T Q (x_k - r_k) ∑ k = 0 N − 1 ( x k − r k ) T Q ( x k − r k ) : This term minimizes the difference between the current state x k x_k x k and the reference r k r_k r k , weighted by the matrix Q Q Q . ( x N − r N ) T Q N ( x N − r N ) (x_N - r_N)^T Q_N (x_N - r_N) ( x N − r N ) T Q N ( x N − r N ) : Similar to the previous term but for the final state at k = N k = N k = N , with a different weighting matrix Q N Q_N Q N . Control effort ...
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