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In this paper we present a novel method to obtain the basic frequency of an unknown periodic signal with an arbitrary waveform, which can work online with no additional signal processing or logical operations. The method originates from non-linear dynamical systems for frequency extraction, which are based on adaptive frequency oscillators in a feedback loop. In previous work, we had developed a method that could extract separate frequency components by using several adaptive frequency oscillators in a loop, but that method required a logical algorithm to identify the basic frequency. The novel method presented here uses a Fourier series representation in the feedback loop combined with a single oscillator. In this way it can extract the frequency and the phase of an unknown periodic signal in real time and without any additional signal processing or preprocessing. The method determines the Fourier series coefficients and can be used for dynamic Fourier series implementation. The proposed method can be used for the control of rhythmic robotic tasks, where only the extraction of the basic frequency is crucial. For demonstration several highly non-linear and dynamic periodic robotic tasks are shown, including also a task where an electromyography (EMG) signal is used in a feedback loop.

The results of this study may be clinically relevant in terms of choice of the percutaneous method used for the repair of the ruptured Achilles tendon.

The paper deals with kinematic control algorithms for on-line obstacle avoidance which allow a kinematically redundant manipulator to move in an unstructured environment without colliding with obstacles. The presented approach is based on the redundancy resolution at the velocity level. The primary task is determined by the end-effector trajectories and for the obstacle avoidance the internal motion of the manipulator is used. The obstacle avoiding motion is defined in onedimensional operational space and hence, the system has less singularities what makes the implementation easiel: Instead of the exact pseudoinverse solution we propose an approximate one which is computationally more eficient and allows also to consider many simultaneously active obstacles without any problems. The fast cycle times of the numerical implementation enable to use the algorithm in real-time control. For illustration some simulation results of highly redundant planar manipulator moving in an unstructured and time-varying environment and experimental results of a four link planar manipulator are given.

In this paper, a method for force control of redundant robots in an unstructured environment is proposed. We assume that the obstacles are not known in advance. Hence, the robot arm has to be compliant with the environment while tracking the desired position and force at the end-effector. First, the dynamic properties of the internal motion of redundant manipulators are considered. The motion is decoupled into the end-effector motion and the internal motion. Next, the dynamic model of a redundant manipulator is derived. Special attention is given to the inertial properties of the system in the space where internal motion is taking place; we define a null-space effective inertia and its inverse. Finally, a control method is proposed which completely decouples the motion of the manipulator into the task-space motion and the internal motion and enables the selection of dynamic characteristics in both subspaces separately. The proposed method is verified with simulation and with experimental results of a four-degrees-of-freedom planar redundant robot.