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The purpose of this paper is to develop a method for multiple soft fault diagnosis of nonlinear circuits including fault detection, identification of faulty elements and estimation of their values in real circumstances.

The method for fault diagnosis proposed here uses a measurement test leading to a system of nonlinear equations expressing the measured quantities in terms of the circuit parameters. Nonlinear functions, which appear in these equations are not given in explicit analytical form. The equations are solved using a homotopy concept. A key problem of the solvability of the equations is considered locally while tracing the solution path. Actual faults are selected on the basis of the observation that the probability of faults in fewer number of elements is greater than in a larger number of elements.

The results indicate that the method is an effective tool for testing nonlinear circuits including bipolar junction transistors and junction field effect transistors.

The homotopy method is generalized and associated with a restart procedure and a numerical algorithm for solving differential equations. Testable sets of elements are found using the singular value decomposition. The procedure for selecting faulty elements, based on the minimal fault number rule, is developed. The method comprises both theoretical and practical aspects of fault diagnosis.

Analysis of piecewise linear resistive networks, described by nodal equations, using the Gauss‐Seidel method is presented in the paper. The conditions which guarantee the existence of a unique solution and convergence of the iterative technique are formulated. An algorithm is described and a numerical example is demonstrated.

Dynamic non‐linear circuits driven by DC voltage and current sources are considered in the paper. The problem of identification of asymptotically stable equilibrium states is analyzed. The circuits are studied where there is a one‐to‐one correspondence between each operating point of a DC model of a dynamic circuit and equilibrium state of the dynamic circuit. A method is developed, based on quantities concerning resistive circuits only, enabling us to select some of the operating points being asymptotically stable equilibrium states. It is shown that these operating points are asymptotically stable equilibrium states of some class of dynamic circuits which differ one from another in characteristics of the capacitors and inductors. The approach is illustrated by a numerical example.

The purpose of this paper is to develop a method for finding all the DC solutions in nonlinear circuits with the thermal constraint.

The proposed approach employs an algorithm for finding all the DC solutions without thermal constraint, including a new contraction and elimination method, an efficient method for tracing characteristics expressing voltages and power in terms of temperature, and electrical analog of the chip thermal behavior.

The paper brings a method that guarantees finding all the DC solutions, considering thermal behavior of the chip, in mid‐scale practical transistor circuits.

A new contraction and elimination method, being the core of the algorithm for finding all the DC solutions, is proposed. An approach enabling us to consider a feedback between the power dissipated inside the chip and the temperature, which affects the circuit parameters and consequently the solutions is developed.

This paper aims to evaluate four different simultaneous localization and mapping (SLAM) systems in the context of localization of multi-legged walking robots equipped with compact RGB-D sensors. This paper identifies problems related to in-motion data acquisition in a legged robot and evaluates the particular building blocks and concepts applied in contemporary SLAM systems against these problems. The SLAM systems are evaluated on two independent experimental set-ups, applying a well-established methodology and performance metrics.

Four feature-based SLAM architectures are evaluated with respect to their suitability for localization of multi-legged walking robots. The evaluation methodology is based on the computation of the absolute trajectory error (ATE) and relative pose error (RPE), which are performance metrics well-established in the robotics community. Four sequences of RGB-D frames acquired in two independent experiments using two different six-legged walking robots are used in the evaluation process.

The experiments revealed that the predominant problem characteristics of the legged robots as platforms for SLAM are the abrupt and unpredictable sensor motions, as well as oscillations and vibrations, which corrupt the images captured in-motion. The tested adaptive gait allowed the evaluated SLAM systems to reconstruct proper trajectories. The bundle adjustment-based SLAM systems produced best results, thanks to the use of a map, which enables to establish a large number of constraints for the estimated trajectory.

The evaluation was performed using indoor mockups of terrain. Experiments in more natural and challenging environments are envisioned as part of future research.

The lack of accurate self-localization methods is considered as one of the most important limitations of walking robots. Thus, the evaluation of the state-of-the-art SLAM methods on legged platforms may be useful for all researchers working on walking robots’ autonomy and their use in various applications, such as search, security, agriculture and mining.

The main contribution lies in the integration of the state-of-the-art SLAM methods on walking robots and their thorough experimental evaluation using a well-established methodology. Moreover, a SLAM system designed especially for RGB-D sensors and real-world applications is presented in details.