The paper "CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design" by Zeji Yi, Chaoyi Pan, Guanqi He, Guannan Qu, and Guanya Shi from Carnegie Mellon University addresses the theoretical understanding and optimization of sampling-based Model Predictive Control (MPC). The authors focus on Model Predictive Path Integral Control (MPPI), a widely used sampling-based MPC method, and provide a detailed convergence analysis. They show that MPPI exhibits linear convergence rates when the optimization is quadratic, which extends to time-varying LQR systems and more general nonlinear systems. The theoretical findings lead to the development of CoVariance-Optimal MPC (CoVO-MPC), an algorithm that optimizes the sampling covariance to enhance convergence rates. Empirical results demonstrate that CoVO-MPC outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor control tasks. The paper contributes to the theoretical understanding of sampling-based MPC and offers a practical and efficient algorithm with significant empirical advantages.The paper "CoVO-MPC: Theoretical Analysis of Sampling-based MPC and Optimal Covariance Design" by Zeji Yi, Chaoyi Pan, Guanqi He, Guannan Qu, and Guanya Shi from Carnegie Mellon University addresses the theoretical understanding and optimization of sampling-based Model Predictive Control (MPC). The authors focus on Model Predictive Path Integral Control (MPPI), a widely used sampling-based MPC method, and provide a detailed convergence analysis. They show that MPPI exhibits linear convergence rates when the optimization is quadratic, which extends to time-varying LQR systems and more general nonlinear systems. The theoretical findings lead to the development of CoVariance-Optimal MPC (CoVO-MPC), an algorithm that optimizes the sampling covariance to enhance convergence rates. Empirical results demonstrate that CoVO-MPC outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor control tasks. The paper contributes to the theoretical understanding of sampling-based MPC and offers a practical and efficient algorithm with significant empirical advantages.