Finite‐Time Control in the Operational Space of Robot Manipulators

ABSTRACT This work proposes novel control methodologies to address the finite‐time regulation problem for robotic manipulators in the Cartesian (operational) space. Conventional robotic control architectures are predominantly designed in the joint space, which requires the use of inverse kinematics to map the desired operational space pose. However, this process can be computationally intensive and may not always yield feasible solutions. Our proposed control schemes are based on the transposed Jacobian approach to circumvent the need for inverse kinematics, enabling direct finite‐time regulation in the operational space with and without bounded torques. In fact, this work extends some classical transposed Jacobian‐based controllers to the finite‐time control setting. The main technical challenge in the control design is that standard homogeneity‐based techniques cannot be applied because the resulting closed‐loop system does not admit a homogeneous approximation. Instead, the stability analysis is conducted via strict Lyapunov functions. Simulation results illustrate the performance of the proposed control schemes.