A diagonal Hestenes–Stiefel conjugate gradient algorithm with iterative complexity analysis and its application in robotic model

Purpose – The mechanization of the meat cutting companies has become essential due to the lack of skilled workers and to working conditions. This paper deals with the analysis of human gestures in order to improve the performance of a redundant robotic cell. The aim is to define optimization criteria linked to the process and the human gesture analysis to improve the cutting process with a redundant robotic cell. Design/methodology/approach – This paper deals with an optimized path planning of complex tasks based on the human arm analysis. The first part details the operator's manual work. The robotized cutting strategy using bones as a guide associated with an industrial force control leads to the tasks redefinition. Thus, the analysis of the arm during the tasks is presented. With a robotic model, the authors evaluate the relevance of two criteria (kinematic and mechanical) that the operator naturally manages. These criteria are used to improve the robotized cutting process by using redundancy. Simulation work and experimentation are presented to show the enhanced performance. Findings – The paper explains how to define optimization criteria based on human arm analysis to realize cutting operations which require force or dexterity performance. It presents a study on the criteria weighting on a robotic arm model established through human arm analysis. The optimized cutting process clearly shows improvement. Research limitations/implications – The scalability of the ham implied the definition of iterative trajectories to follow the curvature of the bone. Due to the use of an industrial force control, no online optimization can be achieved. The off-line optimization implies that the boundary of the trajectory space is technically feasible. Nevertheless, more information has to be extracted from the deboning process such as vision data in order to improve cutting quality. Practical implications – This study was carried out within the framework of several national and European projects (FUI SRDViand, ANR ARMS, FP7 Echord Dexdeb) in collaboration with ADIV (Meat Institute Development Agency). The redundant robotic cell was developed and implemented at ADIV and used for feasibility studies in connection with SME/SMI French sector. Originality/value – The paper deals with the cutting of soft bodies such as meat and complex human gesture analysis, which constitute an innovative challenge for the coming years in order to help or replace humans in industrial meat companies with difficult working conditions.

In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.

In this scholarly investigation, the study focuses on scrutinizing the locomotion and control mechanisms governing a single-legged robot. The analysis encompasses the robot’s movement dynamics pertaining to two primary objectives: executing jumps and sustaining equilibrium throughout successive jump sequences. Diverse concepts of this robot model have been scrutinized, leading to the introduction of a distinctive semi-active model devised for maintaining the robot’s balance. The research involves an initial design for the robot model followed by the introduction of a multi-phase composite control system. As per the proposed model, the jumping action is facilitated through a four-link mechanism augmented by a spring, while balance preservation is achieved through the independent operation of two arms connected to the upper body. To address the successive jumps within the four-link mechanism, a multi-phase feedback controller is engineered. Additionally, a hybrid control strategy, incorporating the Deep Deterministic Policy Gradient algorithm (DDPG) along with a feedback controller, is proposed to sustain balance throughout the robot’s contact and flight phases. The research outcomes, acquired through a series of comprehensive tests conducted within the Simulink simulator environment, demonstrate the robot’s capacity to maintain balance over 80 consecutive jumps. The evaluations encompassed various simulated external disturbances, including 1- horizontal impacts on the upper body, 2- disparities in ground height, and 3- alterations in ground angle between consecutive steps. Notably, the findings showcase the robot’s adeptness in maintaining balance despite an impact with an amplitude of 25 N for a duration of 0.1 seconds, as well as its resilience in managing ground height disparities up to 3 cm and ground angle variations of up to 3°.

Conjugate Gradient (CG) methods are renowned for their efficiency and low memory requirements when solving optimization problems. However, certain formulations of CG methods that switch between two or more CG parameters often overlook specific values that could have been integrated. Moreover, the demonstration of the sufficient descent property in these methods usually relies on a strategy that assumes the possible exclusion of certain function values. To alleviate this assumption, this article introduces a structured Liu–Storey spectral CG method. This method extends the formulation of the spectral Fletcher conjugate descent method, enabling it to maintain fast convergence and inherit a good restart property. Therefore, the method ensures that the sufficient descent property holds without additional requirements and converges globally via some standard assumptions. Additionally, the method proves useful in solving robotic and image reconstruction models. Finally, it demonstrates robustness when compared to some standard algorithms.

This article puts forward a robust model predictive control (MPC) strategy fortified by a learning model within the framework of fully actuated system (FAS) approach. The proposed strategy is crafted to tackle the control difficulties of robotic manipulators under the limitations of joint angles and angular velocities. By leveraging a radial basis function neural network (RBFNN) to offset the inaccuracies in the manipulator’s dynamic modelling, a FAS model with RBFNN is constructed. Based on this, the FAS approach is utilised to formulate the nominal controller, which can efficiently manage the nonlinear and coupled dynamics of the system. To deal with the disparities between the learning model and the actual system dynamics, the robust MPC is incorporated. This also ensures compliance with operating limits and improves the accuracy of the tracking control. Moreover, the iterative feasibility and stability analysis are completed. The effectiveness of the proposed method is validated through simulations with the Franka robotic numerical model.

In this paper we analyze the iteration complexity of a dual fast gradient method for solving general constrained convex problems, that can arise e.g in embedded model predictive control (MPC). When it is difficult to project on the primal feasible set described by convex constraints, we use the Lagrangian relaxation to handle the complicated constraints and then, we apply a dual fast gradient algorithm for solving the corresponding dual problem. We provide sublinear estimates on the primal suboptimality and feasibility violation of the generated approximate primal solutions. The iteration complexity analysis is based on two types of approximate primal solutions: the last primal iterate sequence and an average primal sequence. We also test the performance of the algorithm on MPC for a simplified model of a self balancing robot.

This paper presents a method of optimal path planning for space robots to minimize the total accouter torque required for realizing the final position of the manipulator hand. The proposed method determines the optimum trajectory of joint angles that minimizes the total amount of the output torque to be applied at the joint actuators. In this paper, the nonlinear friction torque inherent to the joint actuator mechanism, as well as the dynamic torque used for the manipulator motion, is modeled in the equations of motion. The optimal control problem is solved by using Fourier series approximation of the trajectories. Thereby the original optimal control problem is reduced to a nonlinear parameter optimization problem, where the Rosenbrock method is used in the cost function minimization. The sequential conjugate gradient and restoration (SCGR) algorithm is also used for improving the Fourier series solutions. Numerical simulations are made for a twodimensional experimental model of free-flying space robot having a three-link rigid manipulator. The results show that the obtained optimum trajectory depends highly on the magnitude of the joint friction torque, which imply the fact that an accurate modeling of the joint friction torque is very important for the optimal path planning.

<div> <h2>Abstract</h2> <p><strong>Objectives:</strong> To study an algorithm to control a bipedal robot to walk so that it has a gait close to that of a human. It is known that the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm is a highly efficient algorithm with a few changes compared to the popular algorithm — the commonly used Deep Deterministic Policy Gradient (DDPG) in the continuous action space problem in Reinforcement Learning.<strong> Methods:</strong> Different from the usual sparse reward function model used, in this study, a reward model combined with a sparse reward function and dense reward function will be proposed. The application of the TD3 algorithm together with the proposed reward function model to control a bipedal robot model with 6 degrees of freedom will be presented. The training process is simulated in Gazebo/Robot Operating System (ROS) environment. <strong>Finding:</strong> The results show that, when choosing a reward model combined with a sparse reward function and a dense reward function suitable for the robot model, will help it learn faster and achieve better results. The biped robot can walk straight with an almost human-like gait. In the paper, the results from the TD3 algorithm combined with the proposed reward model are also compared with the results from other algorithms. <strong>Novelty:</strong> Applying the TD3 algorithm combined with the proposed reward model for the 6-DOF biped robot and simulating the robot’s gait in Gazebo/ROS environment, ROS is a middleware that can be used to control a robot in a real environment in the future.</p> <p><strong>Keywords:</strong> TD3; biped robot; reinforcement learning; ROS; Gazebo</p> </div> <div></div> <div> </div>

The conjugate gradient (CG) method is one of the most popular methods to solve nonlinear unconstrained optimization problems. The Hestenes-Stiefel (HS) CG formula is considered one of the most efficient methods developed in this century. In addition, the HS coefficient is related to the conjugacy condition regardless of the line search method used. However, the HS parameter may not satisfy the global convergence properties of the CG method with the Wolfe-Powell line search if the descent condition is not satisfied. In this paper, we use the original HS CG formula with a mild condition to construct a CG method with restart using the negative gradient. The convergence and descent properties with the strong Wolfe-Powell (SWP) and weak Wolfe-Powell (WWP) line searches are established. Using this condition, we guarantee that the HS formula is non-negative, its value is restricted, and the number of restarts is not too high. Numerical computations with the SWP line search and some standard optimization problems demonstrate the robustness and efficiency of the new version of the CG parameter in comparison with the latest and classical CG formulas. An example is used to describe the benefit of using different initial points to obtain different solutions for multimodal optimization functions.

We propose a Deep learning which is to be aimed at the method of robotic arm modeling algorithm. Firstly, the movement of the mechanical arm, raise the traditional intelligent grasping system, improve the SSD original model, and enhance the backbone network performance selectively, improve the depth of the applicability of deterministic strategy gradient (DDPG) algorithm for further research, to shorten the mechanical arm model debugging time to reach the goal of avoiding obstacles according to research on the mechanical arm dynamics modeling.This will make the robotic arm to have a high ability to adapt to the environment, and can provide researchers with ideas to solve the theoretical research and engineering implementation in this field after training and learning.

A rapidly convergent projected Hestenes-Stiefel conjugate gradient method is presented to help design an novel optimal robust controller of bipedal walking robots. The algorithm converges to a stable periodic gait based on an initial gait. In order to demonstrate the feasibility and effectiveness of the algorithm, we will conduct numerical simulations on the model of 5-link bipedal walking robot. Moreover, computer simulation results further demonstrate the superior performance of the projected Hestenes-Stiefel conjugate gradient algorithm compared with the conventional algorithm. Therefore, it is reasonable to infer that the projected Hestenes-Stiefel conjugate gradient approach can be used in real-time systems.

Based on the Dai and Kou (DK) conjugate gradient (CG) parameter, two spectral CG parameters are proposed using combined strategies. These strategies integrate the quasi-Newton method and the generalized conjugacy condition. To ensure a spectral CG parameter for general functions, one of the spectral parameters generalizes the Zhou-DK (ZDK) method introduced by Faramarzi and Amini (Journal of Optimization Theory and Applications, pp. 667–690, 2019). This method leverages the double-bounded property and truncates a term in the spectral parameter to establish its convergence. Consequently, the combined strategies in this article remove the double-bounded property imposed by the ZDK method. The sufficient descent property of the two spectral methods is achieved independently of line search considerations. Numerical experiments, based on the generalized spectral CG method and using some known test functions, show promising results compared to other popular CG methods. Finally, the method is also applied to solve robotic and image restoration models.

An adaptive array code acquisition for direct-sequence/ code-division multiple access (DS/CDMA) systems was recently proposed to enhance the performance of the conventional correlator-based method. The scheme consists of an adaptive spatial and an adaptive temporal filter, and can simultaneously perform beamforming and code-delay estimation. Unfortunately, the scheme uses a least-mean-square (LMS) adaptive algorithm, and its convergence is slow. Although the recursive-least-squares (RLS) algorithm can be applied, the computational complexity will greatly increase. In this paper, we solve the dilemma with a low-complexity conjugate gradient (LCG) algorithm, which can be considered as a special case of a modified conjugate gradient (MCG) algorithm. Unlike the original conjugate gradient (CG) algorithm developed for adaptive applications, the proposed method, exploiting the special structure inherent in the input correlation matrix, requires a low computational-complexity. It can be shown that the computational complexity of the proposed method is on the same order of the LMS algorithm. However, the convergence rate is improved significantly. Simulation results show that the performance of adaptive array code acquisition with the proposed CG algorithm is comparable to that with the original CG algorithm.

Solving large and sparse linear least-squares problems by conjugate gradient algorithms

Conjugate Gradient (CG) method is the most prominent iterative mathematical technique that can be useful for the optimization of both linear and non-linear systems due to its simplicity, low memory requirement, computational cost, and global convergence properties. However, some of the classical CG methods have some drawbacks which include weak global convergence, poor numerical performance both in terms of number of iterations and the CPU time. To overcome these drawbacks, researchers proposed new variants of the CG parameters with efficient numerical results and nice convergence properties. Some of the variants of the CG method include the scale CG method, hybrid CG method, spectral CG method, three-term CG method, and many more. The hybrid conjugate gradient (CG) algorithm is among the efficient variant in the class of the conjugate gradient methods mentioned above. Some interesting features of the hybrid modifications include inherenting the nice convergence properties and efficient numerical performance of the existing CG methods. In this paper, we proposed a new hybrid CG algorithm that inherits the features of the Rivaie et al. (RMIL*) and Dai (RMIL+) conjugate gradient methods. The proposed algorithm generates a descent direction under the strong Wolfe line search conditions. Preliminary results on some benchmark problems show that the proposed method efficient and promising.