The authors recently introduced a Kalman filter-based approach for estimating noise-contaminated unmodeled signals. However, in that work, the dimension of the Kalman filter depends on the complexity of the signals being estimated, which are not known a priori. This typically requires a trial-and-error process, often resulting in an excessively large filter dimension that complicates the method’s practical application. To overcome this problem, this paper proposes a solution for estimating complex, unmodeled, and noise-contaminated signals while simultaneously obtaining a low-dimensional dynamical model whose output approximates the actual noise-free signal. This is achieved by incorporating a fuzzy error covariance matrix into the standard linear Kalman filter algorithm. The proposed modification prevents the Kalman filter estimate from drifting away from the true signal and provides an alternative to the traditional abrupt resetting of the error covariance matrix. Notably, this modification can be seen as a soft reset of certain initial conditions and, as demonstrated, does not compromise the Kalman filter’s stability. Furthermore, the result shows that incorporating simple fuzzy logic concepts may substantially enhance the performance of some established algorithms.

In this paper, a modification of the classical PID controller scheme for position control is presented. The resulting controller incorporates an exponential trajectory that smoothly guides the system towards the setpoint and a hybrid mechanism to dynamically reset the exponential signal, allowing an adaptive response to discontinuous reference signals. This combination leverages the benefits of exponential trajectories to reduce overshoot and transient oscillations, while the hybrid system ensures robust performance over a wide range of operating scenarios. Among the advantages of the proposed approach, two stand out: (1) significant improvements in energy savings can be achieved in some cases, and (2) closed-loop system performance can be improved even considering poorly tuned PIDs.

The possibility of a robot failing to perform its task can be influenced by factors related to its movement and the load it carries. This concern is particularly important in mobile robots where these factors are more noticeable. Many researchers have conducted studies to quantify the loss of stability in different types of robots. However, these studies often require expensive and complex equipment for replication. Therefore, this research proposes an alternative approach to estimate tip-over stability in a simulated environment made in MATLAB/Simulink. The methodology involves using a 3-degree-of-freedom serial manipulator placed on an angular positioning table which are imported from CAD files respectively. The stability measure is determined by applying a criterion based on the average normal reactions at the base of the manipulator. Case studies are conducted to simulate operating conditions of both systems in order to assess the potential for tipping over based on the trajectory between two desired points. Estimation of tip-over is demonstrated by the values obtained by the reaction of the stability values of each edge of the system and the normalized stability for each case. Limitation of the process is discussed.

For mobile manipulators, tipping-over is one of the most important problems when operating on uneven terrain or manipulating heavy objects. The estimation and evaluation of dynamic stability with an easy-computed measure helps to generate actions to avoid tipping-over. This is particularly important in autonomous systems and in human remotely operated manipulators. Therefore, this research presents a tip-over stability analysis applied to a hybrid mobile manipulator that consists of a mobile platform, a Stewart parallel platform and a serial arm manipulator of three degrees of freedom. This paper evaluates the Mean Normal Ground Reaction (MNGR) criterion for a hybrid mobile manipulator comprising a mobile base, a Stewart parallel platform and a 3-DOF serial arm. The MNGR criterion exhibits low computational complexity while remaining sensitive to top-heaviness. Through simulations and experimental tests, this study demonstrates that dynamically reconfiguring the Stewart platform significantly improves the overall dynamic tip-over stability.