Dual-Quaternion-Based SLERP MPC Local Controller for Safe Self-Driving of Robotic Wheelchairs

Abstract

In this work, the motion control of a robotic wheelchair to achieve safe and intelligent movement in an unknown scenario is proposed. The primary objective is to develop a comprehensive framework for a robotic wheelchair that combines a global path planner and a model predictive control (MPC) local controller. The A* algorithm is employed to generate a global path. To ensure safe and directional motion for the wheelchair user, an MPC local controller is implemented taking into account the via points generated by an approach combined with dual quaternions and spherical linear interpolation (SLERP). Dual quaternions are utilized for their simultaneous handling of rotation and translation, while SLERP enables smooth and continuous rotation interpolation by generating intermediate orientations between two specified orientations. The integration of these two methods optimizes navigation performance. The system is built on the Robot Operating System (ROS), with an electric wheelchair equipped with 3D-LiDAR serving as the hardware foundation. The experimental results reveal the effectiveness of the proposed method and demonstrate the ability of the robotic wheelchair to move safely from the initial position to the destination. This work contributes to the development of effective motion control for robotic wheelchairs, focusing on safety and improving the user experience when navigating in unknown environments.

A Review on the Applications of Dual Quaternions

“…[66] developed, based on dual quaternions, a novel kinematic measure of mean (average) and variance of spacial displacements. Path planning of robots and manipulators are being accomplished through motion interpolation where global poses are defined previously and the path connecting theses poses is derived continuously through the dual quaternion's Screw Linear Interpolation (Screw Linear Interpolation, or sclerp, will be discussed in more detail in Section 5.6) [67][68][69]. Another important work, at the end of the decade, was the hand-eye calibration in [70], which, together with robot-world and robot-robot calibration, is still an active research area in dual quaternions [71][72][73][74][75].…”

“…Later in the same decade, the works of control using dual quaternions appeared as kinematic control [78]. After that, the number of works in this area increased rapidly, featuring dual quaternion PID [79], kinematic control [24,80,81], feedback linearization [82][83][84][85][86], model predictive control [69,87,88], adaptive control [47,89] (ref. [90] used adaptive control to perform kinematic-model-free control, in which no previous knowledge of the kinematic model or even joint variables is required to move the end-effector to the desired pose), sliding modes [91,92], H ∞ [46] and backstepping [93,94].…”

“…In this case, the dual quaternion's Screw Linear Interpolation can be used to accomplish the motion interpolation (or even a C 1 interpolation) (detailed in Section 5.6). That strategy to path planning is taken by [67][68][69].…”