Autonomous electric vehicles (AEVs) have garnered increasing attention in recent years as they hold significant promise for transforming the transportation sector. However, despite advances in the field, effective vehicle drive control remains a critical challenge that must be addressed to realize the full potential of AEVs. This study presents a novel approach to AEV drive control for concurrently generating a suitable speed profile and controlling the vehicle drive speed along a planned path that takes into account various driving circumstances that mimic real-world driving. The designed strategy is divided into two parts: The first part presents a proposed speed planning algorithm (SPA) that works on developing an adequate speed profile for vehicle navigation; first, the algorithm uses an approach for identifying sharp curves on the predefined trajectory; secondly, based on the dynamic properties of these curves, it generates an appropriate speed profile to ensure smooth vehicle travel across the entire trajectory with varying velocities. The second part proposes a new back-stepping control technique with a space vector modulation (SVM) strategy to control the speed of an induction motor (IM) as a traction part of the AEV. A load torque observer has been designed to enhance the speed-tracking task, while the system stability has been proven using Lyapunov theory. Through a series of experiments and simulations using MATLAB/Simulink software and the dSPACE 1104 real-time interface, we demonstrate the effectiveness of the SPA combined with the back-stepping control technique and highlight its potential to advance the field of AEV technology. Our findings have important implications for the design and implementation of AEVs and provide a foundation for future research in this exciting area of study.