This article proposes an observer design for two important variables in the studies of single-leg hopping robot (SLHR), the apex height, and the vertical velocity of SLHR during its stance phase. At first, the Euler–Lagrange (EL) dynamics of SLHR are obtained and apex height is identified in the state-space representation of the EL dynamics. Apex height is the state variable that represents the robot body’s height at the top point, which keeps on changing as the robot functions. Vertical velocity is the velocity of the robot in the vertical direction. An observer design is presented in this article which will estimate these variables when required. The quality of the estimation is validated by the simulation results where the estimation error is zero which means the model output is correct and observer performance is good.

The problem of hybrid force and motion control over unknown rigid surfaces when only joint position measurements are available is considered. To overcome this problem, an extended state high-gain observer is designed to simultaneously estimate the contact force and joint velocities. These estimated signals are in turn employed to design a local estimator of the unknown surface gradient. This gradient is utilized to decompose the task space into two orthogonal subspaces: one for force tracking and the other one for motion control. A simple position Proportional Integral Derivative (PID) and force Proportional Integral (PI) controllers are proposed to track the desired signals. Finally, a mathematical analysis of the closed-loop dynamics is carried out, guaranteeing uniform ultimate boundedness of the position and force tracking errors and of the surface gradient estimation error. A numerical simulation is employed to validate the approach in an ideal scenario, while experiments are carried out to test the proposed strategy when uncertainties and unmodeled dynamics are present.

We establish a separation principle for a class of fractional order time-delay nonlinear differential systems. We show that a nonlinear time-delay observer is globally convergent and give sufficient conditions under which the observer-based controller stabilises the system.

This paper addresses the trajectory tracking control problem of robotic wheelchairs in the presence of modeling uncertainties. The controller has been designed using position and angular measurements. A global ultra-model, or simplified model achieved from flatness considerations is proposed first. This model highly reduces the design complexity of the state estimation and the output feedback control tasks since it groups, as an unknown time-varying disturbance, both the combined effects of all uncertain state-dependent (i.e., endogenous) nonlinearities and those of external (i.e., exogenous) perturbation inputs which are present in the input-to-flat output model of the system. An extended linear high-gain observer, or Generalized Proportional Integral (GPI) observer, is then developed for the simultaneous, though approximate, state and disturbance estimation. The proposed feedback controller combines the global ultra-model and the GPI observers to conform an active disturbance rejection, or disturbance accommodation, control scheme. The simulation results presented in the paper show that the proposed method has a very good tracking performance and robustness in the presence of system uncertainties, external disturbances and noisy corruptions.

Among the many challenges to deal with, when a robot is interacting with its environment, friction at the contact surface and/or at the joints is one of the most important to be considered. In this paper we propose a control algorithm for the tracking of position and force (unconstrained orientation case only) of a manipulator end-effector that does not require the robot model for implementation. This characteristic has the advantage of making it capable to compensate friction effects without any previous estimation. Furthermore, no velocity measurements are needed, and the unit quaternion is employed for orientation control. Experimental and simulation results are provided.

In this paper, we design a position/force controller for cooperative robots during constrained motion. The proposed scheme is based on the knowledge of the manipulator dynamics and does not require measurements of link velocity or end-effector contact forces. A well-known velocity observer and the design of a force observer are used. The validity of the proposed method is verified by means of experimental results.