This paper develops a kernel-adaptive Mittag-Leffler polynomial framework for solving ψ-Caputo fractional optimal-control problems arising in robotic systems. In the proposed formulation, the function ψ is interpreted as a nonlinear operational clock that reshapes the memory structure of the fractional dynamics and influences the distribution of the control effort over physical time. A normalized operational-time transformation is introduced to convert the original ψ-Caputo system into an equivalent Caputo-type representation; at the same time, the physical-time performance index is preserved through the inverse-clock Jacobian. This formulation allows different kernel choices to be incorporated systematically without altering the underlying optimal control structure. For numerical implementation, QR-orthonormalized Mittag-Leffler polynomial bases are constructed to improve stability and conditioning. The fractional integral terms are evaluated analytically by expanding the basis functions in terms of monomials, yielding an efficient finite-dimensional approximation. For the linear planar robotic regulator, the state variables are analytically eliminated, yielding a symmetric positive-definite quadratic programming problem. For the nonlinear two-link manipulator, the same transformation and approximation strategy produce a nonlinear programming formulation. The method is first validated using a manufactured ψ-Caputo benchmark problem, confirming its accuracy and consistency. It is then applied to robotic control examples to examine the effects of kernel selection on terminal accuracy, control energy, physical-time cost, peak actuation, torque profiles, and numerical conditioning. The results demonstrate that the operational clock significantly influences both computational performance and control behavior.