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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.

Developing an efficient second‐order integration method of transient analysis of nonlinear dynamic circuits which overcomes the main drawback of the trapezoidal rule.

Dynamic circuits including transistors and operational amplifiers are considered. A new family of two‐step, second‐order numerical integration algorithms has been developed using a polynomial approximation.

The algorithms have been worked out which are implicit, A‐stable and they depend on a parameter which is allowed to be changed during the computation process according to a proposed strategy. Also the variable step‐size formula has been derived enabling us to eliminate a restarting procedure. The method has been implemented and tested using several representative circuits. It has been compared, both theoretically and via numerical examples, with the alternative well known algorithms: the trapezoidal rule and the backward differentiation formula of order two.

The algorithms developed in the paper are two‐step and second‐order, consequently the step size cannot be too large and the algorithms are not L‐stable.

A new family of two‐step implicit integration algorithms is developed. It can be useful for the analysis and design of electronic circuits.

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.