A high-static--low-dynamic stiffness (HSLDS) vibration isolator based on a tunable nesting-type electromagnetic negative stiffness (NS) mechanism is presented. The stiffness characteristics of the HSLDS system can be tuned by regulating the current in the coil. When the current is zero, the HSLDS system may degenerate into a passive isolator. The distinctive features of this proposed isolation system are demonstrated from two aspects: (1) in contrast to passive isolators, the proposed isolator can further widen the bandwidth of vibration isolation and improve the isolation performance near the natural frequency of the passive system; (2) compared with certain other electromagnetic isolation systems, the proposed system has a more compact structure, heavier load capacity, and higher NS-generating efficiency. The proposed electromagnetic NS mechanism consists of four permanent magnets and four coil windings. Analytical models of the electromagnetic force and the displacement transmissibility are established. To select an appropriate structural parameter for the prototype, the effects of geometric parameters on transmissibility are discussed from a theoretical viewpoint. The vibration isolation performance of the proposed isolator system is verified, and a tuning strategy is investigated through experiments.

The task-space tracking control of robots without the exact knowledge of kinematics and dynamics has been studied before with the assumption that the joint velocities are available for controller designs. However, the velocity measurements can be contaminated by noises, thereby resulting in poor system performance, or even leading to instability problems. Therefore, in this paper, we propose a new tracking controller for robots in the task space without the use of both task-space and joint-space-velocity measurements, under the condition that both the robot kinematics and dynamics are unknown. To overcome these incapacities without the velocity measurements, we introduce the well-known sliding-observer-design techniques to estimate the joint velocities for the purpose of our controller design. Our main concern, i.e., the stability analysis of our controller design incorporated with the siding observer, is presented with the help of Lyapunov-analysis methodology and the sliding-patch concept. Simulation results are presented to show the performance of our controller-observer designs.