An overview of forward dynamics algorithms and their use in open-source engines

Simulation of real-world dynamics is of major importance in testing and verifying developed industrial concepts and solutions, developing and verifying potential control paradigms, scientific research, learning and training tools, or the entertainment industry as a basis for a game engine. The module of the 3D virtual simulator that achieves simulation of the real-world behaviour such as rigid and elastic body dynamics, particle dynamics, fluid dynamics, electrodynamics, magnetism, etc., is often referred to as a dynamics engine or physics engine. The core of the rigid body dynamics (physics) engine is the solution to the forward dynamics problem, which is defined as finding a rigid body's path, velocity, and acceleration for a given input actuating torque and external forces. The past few decades saw a considerable amount of research in robot dynamics modelling, and there are many methods for robot dynamic model development available in the literature. The most commonly used algorithms for solving robot forward dynamics problem are the Composite-Rigid-Body Algorithm (CRBA) [1] and the Articulated-Body Algorithm (ABA) [2]. CRBA and ABA are reduced coordinate methods where known constraints, such as joints, are embedded in the formulation of the equations of motion. Besides reduced coordinate methods, there are maximal coordinate methods using Lagrange multipliers [3-4] to enforce constraints using constraint reaction forces. This paper presents a comprehensive overview of forward dynamics algorithms and their usage in dynamics engines. Special reference is given to the most commonly used algorithms and methods and their advantages and disadvantages depending on the application. Most important software intended for virtual simulation of robots is presented, emphasising free, open-source use. Firstly, brief history and introduction of CRBA, ABA and Lagrange multipliers methods is given, as they are the most commonly used methods employed by dynamics engines. Next, general phases of the simulation process are described. An integral segment in creating a simulation is the definition of the world - a description of the environment and robot models that are to be simulated. Application of the actuation and external forces and torques to the model, detection of collisions between the bodies, constraint solving, forward dynamics computation and integration to obtain velocity and position of the bodies are performed. Each of these aspects is described with special attention to constraint solving and computation of forward dynamics using the algorithms mentioned above. There is a myriad of free and opensource dynamics engines available, and the focus herein is on the most commonly used engines for simulating robots: Open Dynamics Engine (ODE) [5], DART (Dynamic Animation and Robotics Toolkit) [6], Bullet [7], and Simbody [8] as they are present in the two most popular free, open-source robotics simulators Cyberbotics Webots [9] and OpenRobotics Gazebo [10] (Ignition is the successor of Gazebo). It can be concluded that the most used reduced coordinate method in simulators is ABA, while Lagrange multipliers are the most popular maximal coordinate method. ABA is mainly used for simulating open-loop multi-body systems (robot manipulators) where joint constraints are known upfront. In contrast, Lagrange multiplier methods are used where modularity of the simulated model during simulation run-time is crucial. In reality, most dynamic engines have access to both of these methods to ensure the diversity of the simulation processes that can be executed. Presented conclusions are useful for the appropriate selection of available simulation methods depending on the application, as well as within further advancement and development of simulation and verification frameworks for robotic manipulators and rigid body systems

Open-closed Iterative Learning Control Algorithm for Exoskeleton Rehabilitation Purposes

The paper designs an appropriate iterative learning control(ILC) algorithm based on the trajectory characteristics of upper exoskeleton robotic system.The procedure of mathematical modelling of an exoskeleton system for rehabilitation is given and synthesis of a control law with two loops. First (inner) loop represents exact linearization of a given system, and the second (outer) loop is synthesis of a iterative learning control law which consists of two loops, open and closed loop. In open loop ILC sgnPDD2 is applied, while in feedback classical PD control law is used. Finally, a simulation example is presented to illustrate the feasibility and effectiveness of the proposed advanced open-closed iterative learning control scheme.[ https://www.matec-conferences.org/articles/matecconf/pdf/2019/41/matecconf_cscc2019_01010.pdf

Adaptive iterative learning control of robotic system based on particle swarm optimization

In this paper, an adaptive iterative learning control algorithm for robotic manipulators is proposed. A simplified robot manipulator model with 3 degrees of freedom is used as control object for verification purposes. The mathematical model is obtained via Rodriguez approach for modeling differential equations of motion for multi-body systems. The model itself is a simple open-chain kinematic structure. The proposed control system design consists of two layers of controllers. In the inner loop, feedback linearization is applied to deal with the model nonlinearities. Post feedback linearization advanced iterative learning control (ILC) algorithm of sign-D (signum-Derivative) type is introduced as feed-forward compensation with classical PD (Proportional-Derivative) controller in feedback closed loop. A particle swarm optimization (PSO) algorithm is used to optimize ILC gain parameters while gains for PD controller are set by trial and error. Suitable cost function based on position error is chosen for PSO algorithm in order to ensure convergence. Numerical simulation is carried out in two cases – case with constant learning gains and case with PSO optimized learning gains. It is observed that the proposed control law converges to some steady-state error value in both cases

Pljevlja lignite carbon emission charateristics

The anthropogenic emission of GHG especially CO has to be limited and reduced due to their impact on global warming and climate change. Combustion of fossil fuels in the energy sector has a dominant share in total GHG emissions. In order to reduce GHG emission, European Union established a scheme for GHG allowance trading within the community, and the implementation of the European Union emission trading scheme, which is a key to GHG reduction in a cost-effective way. An important part of emission trading scheme is prescribed methodology for monitoring, reporting, and verification of the emission of GHG including characterization of the local fuels combusted by the energy sector. This paper presents lignite characteristics from open-pit mine Borovica-Pljevlja, which has highest coal production in Montenegro (>1.2 Mt per year), including evaluation of its carbon emission factor based on the laboratory analysis of 72 coal samples. Testing of the samples included proximate and ultimate analysis, as well as, net calorific value determination. In accordance with the obtained results, linear correlations between net calorific value and combustible matter content, carbon content and combustible matter content, hydrogen content and combustible matter content, carbon content and net calorific value, were established. Finally, the non-linear analytical correlation between carbon emission factor and net calorific value for Pljevlja lignite was proposed, as a base for the precise calculation of CO emission evaluation

Hybrid pso-newton-raphson algorithm for inverse kinematics problem in robotics

Newton-Raphson method is a deterministic numerical method for solving a system of nonlinear equations. In robotics, it is used to solve inverse kinematics problems. In order to converge towards the optimal solution, the Newton-Raphson method requires a good initial value guess, which can be challenging to obtain. The Particle Swarm Optimization (PSO) algorithm is a stochastic optimization technique for solving nonlinear problems. The advantage of the PSO, in this case, is its ability to search a large amount of data. The PSO can narrow down potential solutions close to the optimal solution and use them as an initial guess for the Newton-Raphson method. Then, the Newton-Raphson method takes over and converges towards the desired optimal solution. In this paper, the feasibility of the hybrid PSO-Newton-Raphson algorithm for solution of robot inverse kinematics problem is investigated for a six-degree of freedom robot arm. All six joints of the robot arm are revolute. The cost function for the PSO algorithm is formed as a function of error between the desired and actual position of the robot arm end-effector. The numerical simulation is carried out to verify the applicability of the proposed concept.[http://cnntechno.com/docs/5_CNN_book_of_abstracts.pdf

Hybrid Pso-Newton-Raphson Algorithm For Inverse Kinematics Problem In Robotics

Abstract: Newton-Raphson method is a deterministic numerical method for solving a system of nonlinear equations. In robotics, it is used to solve inverse kinematics problems. In order to converge towards the optimal solution, the Newton-Raphson method requires a good initial value guess, which can be challenging to obtain. The Particle Swarm Optimization (PSO) algorithm is a stochastic optimization technique for solving nonlinear problems. The advantage of the PSO, in this case, is its ability to search a large amount of data. The PSO can narrow down potential solutions close to the optimal solution and use them as an initial guess for the Newton-Raphson method. Then, the Newton-Raphson method takes over and converges towards the desired optimal solution. In this paper, the feasibility of the hybrid PSO-Newton-Raphson algorithm for solution of robot inverse kinematics problem is investigated for a six-degree of freedom robot arm. All six joints of the robot arm are revolute. The cost function for the PSO algorithm is formed as a function of error between the desired and actual position of the robot arm end-effector. The numerical simulation is carried out to verify the applicability of the proposed concept