Convolutional weighting-enhanced MPC: a comprehensive mathematical framework for energy-efficient quadrotor reference tracking

Model Predictive Control (MPC) is widely adopted across robotic platforms, yet optimal performance hinges on careful tuning of the quadratic cost, where weighting matrices Q and R balance state tracking and control effort. This study introduces a Convolutional Weighting-Enhanced MPC (CMPC) that dynamically adjusts cost weights based on reference deviation by convolving the reference signal with a predefined shaping kernel. The framework applies to standard MPC as well as Nonlinear MPC (NMPC) and Adaptive MPC (AMPC) and related variants. Because the convolution updates Q and R without adding decision variables or a separate optimization layer for weight adaptation, computational overhead is significantly reduced relative to adaptive schemes. Beyond formulation, we rigorously analyze stability and robustness, including CMPC behavior under noise, and we derive sufficient conditions guaranteeing preservation of closed-loop properties. The approach is validated in a quadrotor simulation with two demanding trajectories: one using time-optimal path parameterization and the other employing minimum-snap planning, chosen to stress high-performance motion requirements. We benchmark CMPC against Linear MPC, NMPC, AMPC, and a Linear Quadratic Regulator (LQR). Across scenarios, the convolutional framework consistently yields lower tracking error and reduced energy consumption compared to conventional methods, supporting its suitability for energy-efficient next-generation UAV reference tracking.