This note presents a modification of the integrated friction model structure proposed by Swevers et al. (2000), called the Leuven model. The Leuven model structure allows accurate modeling both in the presliding and the sliding regimes without the use of a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. This note presents two modifications of the Leuven model. A first modification overcomes a recently detected shortcoming of the original Leuven model: a discontinuity in the friction force which occurs during certain transitions in presliding. A second modification, using the general Maxwell slip model to implement the hysteresis force, eliminates the problem of stack overflow, which can occur with the implementation of the hysteresis force.

Technical Note: modification of the Leuven integrated friction model structure

This paper proposes a novel global optimization algorithm called Political Optimizer (PO), inspired by the multi-phased process of politics. PO is the mathematical mapping of all the major phases of politics such as constituency allocation, party switching, election campaign, inter-party election, and parliamentary affairs. The proposed algorithm assigns each solution a dual role by logically dividing the population into political parties and constituencies, which facilitates each candidate to update its position with respect to the party leader and the constituency winner. Moreover, a novel position updating strategy called recent past-based position updating strategy (RPPUS) is introduced, which is the mathematical modeling of the learning behaviors of the politicians from the previous election. The proposed algorithm is benchmarked with 50 unimodal, multimodal, and fixed dimensional functions against 15 state of the art algorithms. We show through experiments that PO has an excellent convergence speed with good exploration capability in early iterations. Root cause of such behavior of PO is incorporation of RPPUS and logical division of the population to assign dual role to each candidate solution. Using Wilcoxon rank-sum test, PO demonstrates statistically significant performance over the other algorithms. The results show that PO outperforms all other algorithms, and consistency in performance on such a comprehensive suite of benchmark functions proves the versatility of the algorithm. Furthermore, experiments demonstrate that PO is invariant to function shifting and performs consistently in very high dimensional search spaces. Finally, the applicability on real-world applications is demonstrated by efficiently solving four engineering optimization problems.

Political Optimizer: A novel socio-inspired meta-heuristic for global optimization

The Sine Cosine Algorithm (SCA) is a population-based optimization algorithm introduced by Mirjalili in 2016, motivated by the trigonometric sine and cosine functions. After providing an overview of the SCA algorithm, we survey a number of SCA variants and applications that have appeared in the literature. We then present the results of a series of computational experiments to validate the performance of the SCA against similar algorithms.

Advances in Sine Cosine Algorithm: A comprehensive survey

Gravitational Search Algorithm (GSA) is an optimization method inspired by the theory of Newtonian gravity in physics. Till now, many variants of GSA have been introduced, most of them are motivated by gravity-related theories such as relativity and astronomy. On the one hand, to solve different kinds of optimization problems, modified versions of GSA have been presented such as continuous (real), binary, discrete, multimodal, constraint, single-objective, and multi-objective GSA. On the other hand, to tackle the difficulties in real-world problems, the efficiency of GSA has been improved using specialized operators, hybridization, local search, and designing the self-adaptive algorithms. Researchers have utilized GSA to solve various engineering optimization problems in diverse fields of applications ranging from electrical engineering to bioinformatics. Here, we discussed a comprehensive investigation of GSA and a brief review of GSA developments in solving different engineering problems to build up a global picture and to open the mind to explore possible applications. We also made a number of suggestions that can be undertaken to help move the area forward.

A comprehensive survey on gravitational search algorithm

Contact mechanics plays an important role in the design, performance analysis, simulation, and control of legged robots. The Hunt-Crossley model and the Coulomb friction model are often used as black-box models with limited consideration of the properties of the terrain and the feet. This paper analyzes the foot-terrain interaction based on the knowledge of terramechanics and reveals the relationship between the parameters of the conventional models and the terramechanics models. The proposed models are derived in three categories: deformable foot on hard terrain, hard foot on deformable terrain, and deformable foot on deformable terrain. A novel model of tangential forces as the function of displacement is proposed on the basis of an in-depth understanding of the terrain properties. Methods for identifying the model parameters are also developed. Extensive foot-soil interaction experiments have been carried out, and the experimental results validate the high fidelity of the derived models.

Foot-terrain interaction mechanics for legged robots: Modeling and experimental validation

This paper presents the implementation of impedance control for a hydraulically driven hexapod robot named COMET-IV, which can walk on uneven and extremely soft terrain. To achieve the dynamic behavior of the hexapod robot, changes in center of mass and body attitude must be taken into consideration during the walking periods. Indirect force control via impedance control is used to address these issues. Two different impedance control schemes are developed and implemented: single-leg impedance control and center of mass--based impedance control. In the case of single-leg impedance control, we derive the necessary impedance and adjust parameters (mass, damping, and stiffness) according to the robot legs' configuration. For center of mass–based impedance control, we use the sum of the forces of the support legs as a control input (represented by the body's current center of mass) for the derived impedance control and adjust parameters based on the robot body's configuration. The virtual forces from the robot body's moment of inertia are adapted to achieve optimal control via a linear quadratic regulator method for the proposed indirect attitude control. In addition, a compliant switching mechanism is designed to ensure that the implementation of the controller is applicable to the tripod sequences of force-based walking modules. Evaluation and verification tests were conducted in the laboratory and the actual field with uneven terrain and extremely soft surfaces. © 2011 Wiley Periodicals, Inc. © 2011 Wiley Periodicals, Inc.

Optimal impedance control based on body inertia for a hydraulically driven hexapod robot walking on uneven and extremely soft terrain

Compliant Walking Control for Hydraulic Driven Hexapod Robot on Rough Terrain

Due to its simplicity and less tedious parameter tuning over other multi-agent-based optimization algorithms, Sine Cosine Algorithm (SCA) has gotten lots of attention from numerous researchers for resolving optimization problem. However, the existing SCA tends to have low optimization precision and local minima trapping effect due to the constraint in its exploration and exploitation mechanism. To overcome this drawback, an extensive version of SCA named Improved Sine Cosine Algorithm (iSCA) has been proposed in this work. The main concept is to introduce a nonlinear control strategy to the existing SCA’s exploration and exploitation process in order to synthesize the algorithm’s strength. The efficiency of this suggested algorithm is assessed using 23 classical well-known benchmark functions and the results are then verified by a comparative study with several other algorithms namely Ant Lion Optimizer (ALO), Multi-verse Optimization (MVO), Spiral Dynamic Optimization Algorithm (SDA) and Sine Cosine Algorithm (SCA). Experimental results show that the iSCA is very competitive compared to the state-of-the-art meta-heuristic algorithms.

An Improved Sine Cosine Algorithm for Solving Optimization Problems

This study introduces a variant of Gravitational Search Algorithm (GSA) for discrete optimization problems, namely, Fast Discrete Gravitational Search Algorithm (FDGSA). The main difference between the proposed FDGSA and the existing Binary Gravitational Search Algorithm (BGSA) is that an agent's position is updated based on its direction and velocity. Both the direction and velocity determine the candidates of integer values for the position update of an agent and then the selection is done randomly. Unimodal test functions, such as De Jong's function, Scwefel's function and Rosenbrock's valley are used to evaluate the performance of the proposed FDGSA. Comparison with BGSA is done to benchmark the proposed FDGSA in terms of speed of convergence and quality of solution. The experimental result shows that the proposed FDGSA converges faster compared to the BGSA.

Addie Irawan

Papers

Optimal impedance control based on body inertia for a hydraulically driven hexapod robot walking on uneven and extremely soft terrain

Compliant Walking Control for Hydraulic Driven Hexapod Robot on Rough Terrain

An Improved Sine Cosine Algorithm for Solving Optimization Problems

A Fast Discrete Gravitational Search Algorithm

Hydraulically Actuated Hexapod Robots