Mobile robotic systems are used in a wide range of applications. Especially in the assistive field, they can enhance the mobility of the elderly and disable people. Modern robotic technologies have been implemented in wheelchairs to give them intelligence. Thus, by equipping wheelchairs with intelligent algorithms, controllers, and sensors, it is possible to share the wheelchair control between the user and the autonomous system. The present research proposes a methodology for intelligent wheelchairs based on head movements and vector fields. In this work, the user indicates where to go, and the system performs obstacle avoidance and planning. The focus is developing an assistive technology for people with quadriplegia that presents partial movements, such as the shoulder and neck musculature. The developed system uses shared control of velocity. It employs a depth camera to recognize obstacles in the environment and an inertial measurement unit (IMU) sensor to recognize the desired movement pattern measuring the user’s head inclination. The proposed methodology computes a repulsive vector field and works to increase maneuverability and safety. Thus, global localization and mapping are unnecessary. The results were evaluated by simulated models and practical tests using a Pioneer-P3DX differential robot to show the system’s applicability.