Mobile manipulators find versatile applications across various fields, leveraging the combination of autonomous functionalities and bilateral teleoperation schemes to enhance the effectiveness of these robotic mechanisms. Regarding teleoperation, command generation involves a leader robot with a few degrees of freedom in a bounded workspace, accompanied by a redundant follower robot operating in an unbounded workspace. This article introduces the concept of Cartesian/articular control for delayed bilateral teleoperation of a mobile manipulator, where the follower robot aims to execute the rate/nonlinear-position commands issued by a human handling the leader robot through a proposed hybrid mapping. We implement a P+d controller applied in Cartesian space for the leader while a controller based on inverse kinematics in joint space is employed for the follower, taking advantage of its redundancy. We then propose a Lyapunov-Krasovskii candidate function to analyze theoretically and numerically the time derivative of the functional on the system trajectories. As a result, we derive the conditions that the proposed hybrid mapping and controller parameters must satisfy to ensure bounded errors. Finally, we statistically evaluated objective metrics from multiple pick-and-place task executions considering time delays to quantify the performance achieved
