A Geometric Assistive Controller for the Users of Wheeled Mobile Robots without Desired States

Wheeled mobile robots e.g., wheelchairs, can depend on indirect and discrete joystick controls from users. Correct steering angle becomes more important when the user should determine the vehicle direction in high velocities. Also, the velocity of the semi-automated vehicle can be given with constant patterns. These issues urge a new assistive controller with different objectives to address these problems. Moreover, the conventional control methods mostly require a desired states or reference trajectory beforehand which completely contradicts how humans operate with spontaneous decisions. In this paper, we propose a novel assistive control strategy to improve vehicle locomotion without using reference states. First, we explain the vehicle kinematics and considered Darboux frame kinematics on a contact point of a virtual wheel and plane. Next, the geometric controller using the Darboux frame kinematics is developed for having smooth trajectories under certain safety objectives. We check our findings in the simulation space with different case studies. Another advantage of this controller is using geometric formulations rather than complex algorithms that make it computationally efficient.