Optimal control theory is often used to numerically design single qubit gates in simulations. Connecting this open-loop optimization approach to gradient-free calibration in experiments is difficult due to the very high dimensionality of the former. Moreover, numerically designed pulses usually show poor performances in an experimental setting due to their sensitive nature toward model parameters. In this two-part talk, we try to explore a new method of systematically connecting optimal control theory with gradient-free calibration in experiments. The first part focuses on building robust single-qubit gates for transmon qubits using perturbation theory techniques. We demonstrate that single qubit gates built using this approach are robust to instabilities in control amplitude, dephasing noise and leakage errors and compare the stability performance of our pulse with default DRAG and composite pulses.