In this paper, a velocity estimator is introduced, which results in low-delay and low-noise velocity estimation based on the sampled-quantized position measurement. The method maintains its efficiency for a broad range of velocities and excitation frequencies. The algorithm is computationally efficient and operates well at virtually any sampling frequency. Better velocity observation, increases the efficiency of virtual dampers employed in impedance control; hence, the system remains stable at higher values of virtual stiffness. This work is supported by simulations and experiments.

There are many applications for which a robotic device is used to recreate the sense of touch for a physical or virtual environment. Transparency and stability are two major issues in controlling haptic devices. Transparency highly depends on the quality of state observation while the stability range is mainly affected by the time-delay and sampling frequency. The control force is calculated based on the model of the environment and usually is a function of the position and the velocity at the joints. Optical encoders are commonly used for position measurement because of their high resolution, robustness to noise, and high bandwidth. The velocity, however, is usually determined by differentiating the position data over time which can be noisy at high frequencies. This noise demotes the transparency and stability. Low-pass filters are widely used to filter the noise but they make the system slow and conservatively introduce time-delay which further limits the stability range. In this paper, the method of Adaptive Frequency Differentiation (AFD) is introduced, which operates at varying frequencies and effectively removes the noise caused by the error in position data. The AFD is optimized to operate at its best performance while maintaining the reliability of the differentiation. The output of the AFD is derived by logically interpreting the available data and does not involve iterative loops, which improves the processing time. An extension to this method allows to compute low-delay and noiseless acceleration directly from the position data. The claims of this paper are supported by simulation and experimental results.

In this paper, a nonlinear signal-processing scheme is developed for robotic systems that exploits a joint state-parameter formulation for simultaneous recursive estimation of the states (e.g. joint angles and rates) and uncertain parameters (e.g. inertial and friction parameters), out of noisy measurements (e.g. joint angles). Unscented Kalman filtering was employed to overcome restrictions such as linearity in the parameters and the need for availability of joint velocities and accelerations (present in linear recursive least square methods), and the linearization problems associated with extended Kalman filtering. Owing to the unscented transform concept which requires only input-output evaluations of the dynamic model, a more general and modular implementation is realizable. This allows for the utilization of computational modeling tools without the requirement of symbolically manipulating or deriving the equations of motion. Also, the recursive nature of the scheme allows for both offline processing and online implementation. The practical performance of the proposed scheme was verified through an experiment involving a five-bar linkage based haptic device configured to render a virtual box. The torque pair commands generated by the haptic controller to render the virtual box and the encoder angular measurements acquired through the experiment were processed twice in two different input-output directions: once, for state-parameter estimation of the robot; and, another time for identification of supposedly unknown environmental parameters. Results demonstrate successfulness of the scheme for recursive state-parameter estimation of the robot and the environment, as well as promising applicability in online settings.

Digitally controlled systems are getting more and more popular mainly because of their flexibility and convenience but their stability is strongly affected by the time delay introduced by different factors. For common PID type digital controllers, zero-order holds (ZOHs) are commonly employed and the stability characteristics are investigated based on that concept. Mathematical investigations show that higher-order holds may improve the stability and performance of the system and can reduce the steady state errors significantly. This is because the controller tries to learn from the history of the behavior of the system and then predict the behavior for the time period between sampling instances and generate the best possible control force. Furthermore, a new concept of Modified Holds is introduced, which clearly improves the performance of a digital controller. For most control algorithms this does not prolong the processing time significantly (e.g. less than 1%) which can be neglected in the calculations. The varying control force would need an analogue circuitry to follow the proper curve, which might make the controller's electronic circuits more complex. This can be avoided considering that in almost all digital controllers the main core operates at several orders of magnitude higher frequency than that of the control loop itself. Hence, the control force can also be generated digitally at much higher frequencies. In this paper, after investigating the stability of a 1-DoF system equipped with discrete-time PD controller with first and second order holds, the concept of modified holds is introduced and then the results are validated by simulations. Furthermore, the concept is practically implemented on a self-balancing motor bike robot and the experimental results further support the claims of the paper.