Quaternion-based smooth motion planning for robotic arms

This work presents a comprehensive study on quaternion-based smooth motion planning for robotic arms, emphasizing accurate and continuous orientation control in complex tasks. It begins by highlighting the limitations of traditional Euler-angle and rotation-matrix approaches, such as gimbal lock and interpolation inefficiencies, and introduces quaternions as a robust alternative for representing 3D rotations. The book covers fundamental concepts of robotic kinematics, quaternion algebra, and advanced interpolation techniques like SLERP and SQUAD to achieve smooth and continuous trajectories. It further explores time-parameterized trajectory planning in SE(3), multi-degree-of-freedom synchronization, and blending methods for seamless motion between waypoints. Quaternion-based control strategies, including feedback and PD control, are discussed along with singularity avoidance and robustness in dynamic environments. The work also evaluates performance through simulation and real-time experiments using platforms like MATLAB and ROS, and concludes with applications in industrial, medical, and humanoid robotics, highlighting future trends such as AI-driven and learning-based motion planning.