An Efficient Optimal Control Framework for Robotic Systems Using Mittag‐Leffler Polynomial Techniques

ABSTRACT This article presents a comprehensive overview of optimization‐based modeling and control strategies in robotics, highlighting their evolution over the past three decades. Robotic systems are increasingly designed and controlled through optimization frameworks that integrate dynamic and kinematic analyses, enabling efficient performance across diverse tasks. A key focus is formulating optimal control problems that incorporate nonlinear dynamics, contact interactions, and a wide range of system constraints. The general optimal control problem is formalized using differential‐algebraic equations to capture both continuous dynamics and discrete constraints, providing a unified structure for motion planning. To address the problem, we establish an explicit expression for the Riemann‐Liouville fractional integral operational matrix of Mittag‐Leffler polynomials for the first time, utilizing the Fourier Transform. By utilizing the operational matrix in conjunction with the Galerkin method, the problem is converted into a system of algebraic equations. Ultimately, the effectiveness and precision of the proposed numerical algorithm are demonstrated through several illustrative case studies.