# Efficient method for robot forward dynamics computation (2023)

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## Mechanism and Machine Theory

Volume 145,

March 2020

, 103680

Author links open overlay panelVladimirKvrgicaPersonEnvelopeJelenaVidakovicbEnvelope

## Abstract

Conventional methods for solving robot forward dynamics are characterized by high computational complexity. Recursive Newton-Euler algorithm (RNEA) is the most efficient computational method used for deriving a manipulator's dynamic equations of motion. In order to solve robot forward dynamics using RNEA in the most widely used Walker and Orin's method 1, it is necessary to execute RNEA n + 1 times, where n is the number of degrees-of-freedom (DoF). Herein, a simple and efficient method to solve forward dynamics using the modified RNEA (mRNEA) only once is presented. The proposed method is significantly more beneficial when used for robot simulations as it does not require calculating joint torques as inputs for forward dynamics unlike other methods. Further, an algorithm that calculates the joints’ accelerations based on forward dynamics while considering the actuators’ force/torque saturations and achieves a realistic simulation of robot movements is presented. The proposed mRNEA, its application in the presented forward dynamics algorithm, and the efficiency of the presented algorithms are demonstrated using a serial 6-DoF robot as an example.

(Video) Modern Robotics, Chapter 8.1: Lagrangian Formulation of Dynamics (Part 1 of 2)

## Introduction

One of the goals of robot simulation is to verify the feasibility of programmed movements, and if necessary, to modify them. This is essential in robot design as the real values of forces and moments acting on robot links and joints must be calculated. Identifying the computational efficiency (number of computations) of the algorithms used within the simulation and the design of the robot and multibody systems is very important. The ease of development and implementation (algorithm development for a specific robot) of an algorithm is another highly pertinent feature; it is more important than computational complexity owing to the development of modern-day computers. Further, this is critical with regard to the development of highly complex robot dynamic models.

The past few decades saw a considerable amount of research on the computational efficiency of robot dynamic models within the design, control, and simulation of a variety of very complex and high-speed robots and multibody systems. The simulations used branched kinematic trees and dozens of DoF [1].

Two main problems related to the robot dynamics are forward and inverse dynamics problems. Forward dynamics (FD) solves the motion from the forces, while inverse dynamics (ID) solves the forces from the motion [2]. ID is used in dynamic model-based control and for FD calculations. FD is used mainly in simulation purposes.

One of the present challenges in robot simulation is to derive algorithms that are not only computationally efficient, but also are easy to apply to a specific robot as well.

A Lagrange formulation (LF) of manipulator equations of motion provides a compact analytical form containing a symmetric, non–singular n × n generalized robot mass (inertia) matrix H(q), and a bias vector u′ that denotes joint torque contributions that do not correlate with the joint accelerations [1], [3], [4], [5], [6], [7], [8], [9], [10]]. Therefore, when the LF is used, the joint accelerations $\stackrel{¨}{\mathbf{q}}\left({t}_{k}\right)$ (within one interpolation cycle) can be computed by solving the system of n linear equations, where n is number of manipulator DoF. Although it is not complex to solve FD using LF, this method is typically used for manipulators when n ≤ 3 because of the very high computational complexity of the LF: O(n4).

Robot dynamic models should have a clear relationship with a recursive set from which the optimum computational efficiency is obtained [3]. In contrast to the LF, the computational complexity of the RNEA is O(n). Reference [11] developed a recursive LF; however, the computational complexity of the recursive LF is O(n3).

Luh, Walker, and Paul [12] developed a computationally efficient RNEA which is independent of the type of robot configuration. This method involves successive transformations of the velocities and accelerations from the base of the manipulator out to the end effector, link-by-link, using the relationships of moving coordinate systems. Forces and moments are then computed recursively from the end effector to the base in order to obtain the joint torques/forces (ID). The RNEA can also be found in many classical robotics texts [9], [13], [14], [15], [16].

Walker and Orin [6], [7] employed the RNEA for computing the FD and presented four methods to solve the joint accelerations. Their method 1 (WO method 1) remains the simplest and the most recommended in the literature [3], [4]. According to this method, torque u′ is computed using the RNEA. Further, each column hi, i = 1 to n, of matrix H is computed as the torque vector given by the RNEA. It is shown that WO method 3—later named the Composite-Rigid-Body Algorithm (CRBA) [1], [10], [17]—is the most efficient of all WO methods. Unfortunately, CRBA is difficult to develop and implement.

In this paper, a modified recursive Newton-Euler method for derivation of dynamic model of robot manipulator is proposed. Besides being efficient and easy to use, mRNEA gives explicitly the mass matrix H and the bias vector u′.

For the computation of the mass matrix, [18] developed an Articulated Body Algorithm (ABA) for the FD calculation. The algorithm is based on recursive formulas involving quantities called articulated-body inertias, which represent the inertial properties of the collections of rigid bodies. Reference [19] described an algorithm that reduces the time complexity for the construction of matrix H and inverts it to the theoretical minimum using the RNEA and ABA. The calculation of the terms of the generalized matrix H by means of the Hessian of the Gibbs function with respect to generalized accelerations and a recursive algorithm is presented in [20]. In [21] and [22], it is shown that conventional methods which employ the matrix H [6] can be significantly accelerated by applying suitable factorization.

A parallel algorithm, based on the composed rigid-body method, that generates the matrix H using the parallel Newton–Euler (NE) algorithm, the parallel linear recurrence algorithm, and the modified row-sweep algorithm is described in [23].

Reference [24] presented a parallel computer algorithm for the simulation of large articulated robotic systems. The method employs the Divide and Conquer Algorithm (DCA) multibody methodology and achieves significant increases in speed by using a variation of the ABA to efficiently construct the DCA subsystems.

A methodology for the dynamic modelling of hybrid robots that are constructed by serially connected non-redundant parallel modules is presented [25]. The proposed methods give the inverse dynamics model using RNEA, whereas the forward dynamics model generalizes the serial robot algorithm of Featherstone [18].

An analytical derivation of the matrix H and its inverse for an open-loop, serial-chain robot is presented in [26], [27], [28]. A decomposition of a generalized matrix H based on Decoupled Natural Orthogonal Complement (DeNOC) matrices is used in these papers, which resulted in efficient O(n) recursive FD algorithms that calculate the joint accelerations which are then integrated numerically to perform a simulation [29], [29], [30] (Table2). In [31] and [32], the DeNOC-based formulation is extended to dynamic modelling and the analysis of more complex tree-type robotic systems consisting of multiple-DoF joints.

In [32], a more efficient O(n) recursive FD algorithm based on DeNOC is presented. However, the mechanism—with which the researchers almost halved the number of counts with regard to algorithms presented in papers [29] and [30] —was not discussed. These algorithms are also based on DeNOC considering that they applied this algorithm to a robot that was not a tree type and had only six 1-DOF joints. In [33], a dynamic modelling methodology is presented for parallel multibody mechanical systems based on the RNEA and the DeNOC matrices. This methodology facilitates both ID and FD.

In [34], by using a virtual spring approach, a modified DeNOC method is introduced for forward dynamic analysis of parallel robots.

A general and effective method to solve the forward and inverse dynamics of mechanical systems subjected to nonholonomic constraints is proposed in [35]. In [36] was examined the modular development of two alternate methods for distributed computation of the forward dynamics simulations of constrained mechanical systems. Reference [37] proposed a reduced-order FD of multi-closed-loop systems by exploiting the associated inherent kinematic constraints at the acceleration level.

Reference [38] presented the decomposition of the generalized matrix H of multibody systems with an open kinematic architecture (serial or tree type) with its application in FD and for simulation purposes.

References [39], [40] presented an algorithm which calculates FD for a 3-DoF centrifuge motion simulator and a 4-DoF spatial disorientation trainer using the RNEA only once.

In [41], a numerical algorithm for iterative solution of systems of nonlinear ordinary differential equations for solving forward dynamics problems of manipulators is presented.

Reference [42] considered fuzzy uncertainty in forward dynamics simulations.

The identification of the robot dynamic parameters was investigated in many robotics texts [43], [44], [45], [46].

The aim of this study is to discretize the FD computation and to further reduce the complexity of FD in open-chain manipulators. The contributions of this manuscript are as follows:

(1)

A method to simplify the development and implementation of FD algorithms, which executes the mRNEA only once, is proposed. The terms of the matrix H and the vector u′ are obtained explicitly by using mRNEA in a similar manner as LF.

(2)

An implementation of a new FD algorithm within a simulation system is presented. In the most recommended methods presented in the literature, the additional calculation of the input joint torques u, Eq.(2), had to be performed within this simulation system of a robot. With the presented method, input-joint-torque calculation is performed within the FD algorithm, and therefore, the computational complexity of the simulation system is additionally reduced. As a result, the simulation system has to solve ID only once within each interpolation cycle, in comparison to simulation systems which use, for example, WO method 1, and which solve ID n + 2 times.

(3)

The robot motion equations are discretized in order to be suitable for implementation within discrete simulation systems and robot controllers. This enables the calculations of joint velocities and positions, after the calculation of joint accelerations, in a simple way (Point 7 in Algorithm1).

(4)

The development of the proposed mRNEA and its application in the FD algorithm is systematically illustrated for the cases of serial-chain robots with six and four rotational DoF.

(5)

The presented FD algorithm is computationally one of the most efficient when compared with other methods given in the literature. While the computational complexity of all WO methods, including CRBA, is O(n2) [4], the presented algorithm is of O(n) complexity.

(6)

Compared with other efficient methods, the presented algorithm is very simple to develop and implement for a general open-chain robot.

(7)

Finally, an algorithm is presented herein which examines the joint acceleration capabilities in each interpolation cycle considering the actuator torque/force saturations and provides realistic values of the accelerations along with the velocities, positions, forces, and moments of the robot links during programmed movements (Algorithm1).

The rest of the paper is organized as follows. In Section2, mathematical background for the research interest of the paper is given. Section3 presents the proposed approach for efficient FD calculation and its implementation in a robot simulation system. Section4 depicts the proposed FD algorithm for open-chain manipulators with n DoF. The application of FD, based on mRNEA on an open-chain 6-DoF system, is given systematically in Section5. A toy model for the 4-DoF spatial disorientation trainer (SDT) is also presented in this Section. The computational efficiency of the proposed FD algorithm is analysed in Section6. The FD algorithm, which calculates the achievable motor velocities in each interpolation cycle based on the actuator torque/force saturations, is presented in Section7. The validity of the proposed algorithm is examined within the simulation system of a 6–DoF serial–chain robot in Section8. Finally, concluding remarks are given in Section9.

## Mathematical background

Given that the motion control and simulation of robots and general multibody systems is performed using discrete controllers (digital computers), the motion equations of such continuous systems need to be discretized to be suitable for numerical calculations and implementation within discrete simulation systems and controllers.

Forward dynamics (FD) calculates the joint accelerations $\stackrel{¨}{\mathbf{q}}\left({t}_{k}\right)$ at a time instant tk and the joint velocities $\stackrel{˙}{\mathbf{q}}\left({t}_{k+1}\right)$ of the next interpolation cycle time (Δt) and joint

## Proposed approaches

Regardless of the type of robotic movements—continuous (controlled) path movement (CP) or point–to–point movement (PTP)—or of the manner in which these movements are given—programmed, hand–guided, vision–guided, or computer-aided design (CAD)–guided—a path planner of the robot controller transforms the motion commands into a series of successive positions of robot joints/actuators. As they are sent to the servo controller at constant time intervals Δt, they correspond to the desired

(Video) Efficient Computing for Robotics and AI

## Proposed FD algorithm based on mRNEA

In this section, the proposed FD algorithm based on mRNEA for open–chain manipulators with n DoF is presented.

A 4 × 4 homogenous transformation matrix (HTM) that transforms point coordinates from frame j to frame i is denoted by jTi, and from the base frame to frame i by Ti. The matrix jTi contains a 3 × 3 orientation matrix ${}^{j}{\mathbf{D}}_{i}=\left[\begin{array}{ccc}{}^{j}{\mathbf{x}}_{i}& {}^{j}{\mathbf{y}}_{i}& {}^{j}{\mathbf{z}}_{i}\end{array}\right]$ and a 3 × 1 position vector jpi.

The linear acceleration of the robot link i centre of mass is${\stackrel{˙}{\mathbf{v}}}_{i}^{\text{cm}}={\left[\begin{array}{ccc}{\stackrel{˙}{v}}_{xi}^{\text{cm}}& {\stackrel{˙}{v}}_{yi}^{\text{cm}}& {\stackrel{˙}{v}}_{zi}^{\text{cm}}\end{array}\right]}^{\mathrm{T}}={\stackrel{˙}{\mathbf{v}}}_{i}+{\stackrel{˙}{\mathbit{\omega }}}_{i}×{\mathbf{r}}_{i}^{\text{cm}}+{\mathbit{\omega }}_{i}×\left({\mathbit{\omega }}_{i}×{\mathbf{r}}_{i}^{\text{cm}}\right),$where ${\mathbf{r}}_{i}^{\text{cm}}$

## Calculation of vectors bik and bikj of 6–DoF serial–chain robot

Herein, the calculation of ${\stackrel{˙}{\mathbf{v}}}_{i}^{cm}$, Eq.(5), of a 6–DoF serial–chain robot as a function of the vectors bik and bikj, needed for the calculation of vectors ei andeik, Eqs.(13)–(15), is systematically presented.${\stackrel{˙}{\mathbf{v}}}_{1}^{cm}={\mathbf{b}}_{11}{\stackrel{¨}{q}}_{1}+{\mathbf{b}}_{111}{\stackrel{˙}{q}}_{1}^{2}$${\stackrel{˙}{\mathbf{v}}}_{2}^{cm}={\mathbf{b}}_{21}{\stackrel{¨}{q}}_{1}+{\mathbf{b}}_{22}{\stackrel{¨}{q}}_{2}+{\mathbf{b}}_{211}{\stackrel{˙}{q}}_{1}^{2}+{\mathbf{b}}_{212}{\stackrel{˙}{q}}_{1}{\stackrel{˙}{q}}_{2}+{\mathbf{b}}_{222}{\stackrel{˙}{q}}_{2}^{2}$${\stackrel{˙}{{\mathbf{v}}^{\prime }}}_{i}={\mathbf{b}}_{i1}{\stackrel{¨}{q}}_{1}+{\mathbf{b}}_{i2}{\stackrel{¨}{q}}_{2}+{\mathbf{b}}_{i3}{\stackrel{¨}{q}}_{3}+{\mathbf{b}}_{i11}{\stackrel{˙}{q}}_{1}^{2}+{\mathbf{b}}_{i12}{\stackrel{˙}{q}}_{1}{\stackrel{˙}{q}}_{2}+{\mathbf{b}}_{i13}{\stackrel{˙}{q}}_{1}{\stackrel{˙}{q}}_{3}+{\mathbf{b}}_{i22}{\stackrel{˙}{q}}_{2}^{2}+{\mathbf{b}}_{i23}{\stackrel{˙}{q}}_{2}{\stackrel{˙}{q}}_{3}+{\mathbf{b}}_{i33}{\stackrel{˙}{q}}_{3}^{2},\phantom{\rule{0ex}{0ex}}i=3,4,5,6$${\stackrel{˙}{\mathbf{v}}}_{3}^{cm}={\stackrel{˙}{{\mathbf{v}}^{\prime }}}_{3}$${\stackrel{˙}{{\mathbf{v}}^{″}}}_{i}={\mathbf{b}}_{i4}{\stackrel{¨}{q}}_{4}+{\mathbf{b}}_{i14}{\stackrel{˙}{q}}_{1}{\stackrel{˙}{q}}_{4}+{\mathbf{b}}_{i24}{\stackrel{˙}{q}}_{2}{\stackrel{˙}{q}}_{4}+{\mathbf{b}}_{i34}{\stackrel{˙}{q}}_{3}{\stackrel{˙}{q}}_{4}+{\mathbf{b}}_{i44}{\stackrel{˙}{q}}_{4}{\stackrel{˙}{q}}_{4}$${\stackrel{˙}{\mathbf{v}}}_{4}^{cm}={\stackrel{˙}{{\mathbf{v}}^{\prime }}}_{4}+{\stackrel{˙}{{\mathbf{v}}^{″}}}_{4}$${\stackrel{˙}{{\mathbf{v}}^{″\prime }}}_{i}={\mathbf{b}}_{i5}{\stackrel{¨}{q}}_{5}+{\mathbf{b}}_{i15}{\stackrel{˙}{q}}_{1}{\stackrel{˙}{q}}_{5}+{\mathbf{b}}_{i25}{\stackrel{˙}{q}}_{2}{\stackrel{˙}{q}}_{5}+{\mathbf{b}}_{i35}{\stackrel{˙}{q}}_{3}{\stackrel{˙}{q}}_{5}+{\mathbf{b}}_{}$

## Computational efficiency

A detailed description of the computational efficiency calculation (counted arithmetic operations for all terms) of the proposed FD algorithm as applied to RL15 is provided in TableC1.

In TableC1, it is shown that the numbers of computations to obtain the joint accelerations of 6–DoF robot RL15 are 1480 M and 1152 A (here, M stands for multiplications/divisions, and A stands for additions/subtractions). In order to compare the computational complexity of the presented algorithm with similar

## FD algorithm relative to manipulator actuators

Similar to Eq.(1), the motion equations for the manipulator relative to the torques/forces of the robot actuators can be written as${\mathbf{H}}_{a}\left(\mathbf{q}\right)\stackrel{¨}{\mathbf{q}}+{{\mathbf{u}}^{\prime }}_{\mathrm{a}}\left(\mathbf{q},\stackrel{˙}{\mathbf{q}},{\mathbf{k}}_{\mathrm{e}\mathrm{a}}\right)={\mathbf{u}}_{\mathrm{a}},$${{\mathbf{u}}^{\prime }}_{\mathrm{a}}\left(\mathbf{q},\stackrel{˙}{\mathbf{q}},{\mathbf{k}}_{\text{ea}}\right)={\mathbf{C}}_{\mathrm{a}}\left(\mathbf{q},\stackrel{˙}{\mathbf{q}}\right)\stackrel{˙}{\mathbf{q}}+{\mathbf{g}}_{\mathrm{a}}\left(\mathbf{q}\right)+\mathbf{J}{\left(\mathbf{q}\right)}^{\mathbf{T}}{\mathbf{k}}_{\text{ea}}+{\mathbf{F}}_{v}\stackrel{˙}{\mathbf{q}}+{\mathbf{F}}_{s}\text{sign}\left(\stackrel{˙}{\mathbf{q}}\right).$

Herein, Ha(q), ${{\mathbf{u}}^{\prime }}_{\mathrm{a}}\left(\mathbf{q},\stackrel{˙}{\mathbf{q}},{\mathbf{k}}_{\text{ea}}\right)$, and ua relate to the actuator rotors; terms ${u}_{\mathrm{a}i}^{\prime }$ and ${h}_{\mathrm{a}ij}$ for the RL15 are given in AppendixD. Fv denotes an n × n diagonal matrix of viscous friction coefficients fvi. The static friction torques are considered as Coulomb friction torques; Fs is an n × n

## Results: verification of proposed FD algorithm

The proposed FD algorithm was tested during a simulation of different movements of the RL15 within its simulation system. The considered application program consists of 13 movements of the RL15 (the end effector path is shown in Fig.A4). In the first 10 movements, the end effector moves along the path without stopping. The first movement is PTP, the next nine are CP, and the last three are PTP movements.

The maximum link angular velocities and accelerations of the RL15 for axes i = 1 to 6 are

## Conclusions

Dynamic model–based robot simulation is necessary for the correct simulation of robot movements. In order to check if the desired joint velocities are feasible, a dynamic model–based robot simulation system relies on a robot FD model and computes the joint accelerations in every interpolation cycle.

In this study, the mRNEA that gives the mass matrix H and the bias vector u′of a dynamic model was explicitly presented. Consequently, the proposed mRNEA allows for solving FD by calculating ID only

## Acknowledgments

This research is supported by the Ministry of Education, Science and Technological Development of Serbia under the project “Development of devices for pilot training and dynamic simulation of modern fighter planes flights: 3DoF centrifuge and 4DoF spatial disorientation trainer” (2011–2019), no. TR 35023.

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(Video) Stanford Seminar - Computational Design of Compliant, Dynamical Robots, Cynthia Sung

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## FAQs

### What is forward dynamics in robotics? ›

Description. The Forward Dynamics block computes joint accelerations for a robot model given a robot state that is made up of joint torques, joint states, and external forces. To get the joint accelerations, specify the robot configuration (joint positions), joint velocities, applied torques, and external forces.

What is the dynamic equation of robot? ›

The equation of motion for a robot mechanism can be written \tag{1} \boldsymbol{\tau} = \boldsymbol{H}(\boldsymbol{q}) \ddot{\boldsymbol{q}} + \boldsymbol{c}(\boldsymbol{q},\dot{\boldsymbol{q}},\boldsymbol{f}_{\!

What are all the algorithms used in robot dynamics? ›

Three main algorithms are described: the recursIve Newton-Euler formulation for inverse dynamics (the calculation of the forces given the accelerations), and the composite-rigid-body and articulated-body methods for forward dynamics (the calculation of the accelerations given the forces).

What is forward dynamics model? ›

In contrast to inverse dynamics where the motion of the model was known and we wanted to determine the forces and torques that generated the motion, in forward dynamics, a mathematical model describes how coordinates and their velocities change due to applied forces and torques (moments).

How do you calculate robot forward kinematics? ›

1. First you have to attach frames to the links when the robot is in home position.
2. Then calculate the transformation matrices of the adjacent frames from base to the end-effector.
3. Next, multiply all the transformation matrices in correct order to get the final transform matrix T0ee.

What is forward dynamic simulation? ›

A forward dynamics simulation is the solution (integration) of the differential equations that define the dynamics of a musculoskeletal model. By focusing on specific time intervals of interest, and by using different analyses, more detailed biomechanical data for the trial in question can be collected.

How do you calculate dynamics? ›

Place your object on a regular scale and find its weight. Multiply its weight by 4.45 to convert from pounds to Newtons. Divide this number by 9.81 (the rate of gravity) to find its mass. Find the velocity of your object and divide that by the time it took your object to reach its destination.

What are the 4 most common types of robots? ›

The six most common types of robots are autonomous mobile robots (AMRs), automated guided vehicles (AGVs), articulated robots, humanoids, cobots, and hybrids.

What are the 4 basic components of a robot? ›

Basic Components of a Robot

The components of a robot are the body/frame, control system, manipulators, and drivetrain. Body/frame: The body or frame can be of any shape and size. Essentially, the body/frame provides the structure of the robot.

What are 3 types of programming methods used for robots? ›

Robot Programming Methods
• Teach Method. This is by far the most popular standard method of programming a robot. ...
• Joint Co-ordinates. The robot joints are driven independently of each other in the required direction. ...
• Global Co-ordinates. ...
• Tool Co-ordinates. ...
• Workpiece Co-ordinates. ...
• Lead Through. ...
• Off-line Programming.

### What are 5 examples of algorithms? ›

Examples of Algorithms in Everyday Life
• Tying Your Shoes. Any step-by-step process that is completed the same way every time is an algorithm. ...
• Following a Recipe. ...
• Classifying Objects. ...
• Bedtime Routines. ...
• Finding a Library Book in the Library. ...
• Driving to or from Somewhere. ...
• Deciding What to Eat.
18 Aug 2022

What is forward kinematics equation? ›

Forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters.

What is an example of a dynamic model? ›

Probably one of the most famous examples of a dynamic systems model is the Lotka–Volterra equations from chemistry and biology, commonly used to explain the interactions between predator and prey in an ecological system. These modeling efforts also find applications in the social sciences.

What is the difference between forward and inverse dynamics? ›

The problem of reconstructing the internal forces and/or torques from the movements and known external forces is called the 'inverse dynamics problem', whereas calculating motion from known internal forces and/or torques and resulting reaction forces is called the 'forward dynamics problem'.

What are the 4 kinematic formulas? ›

There are four basic kinematics equations:

v = v 0 + a t. Δ x = ( v + v 0 2 ) t. Δ x = v 0 t + 1 2 a t 2. v 2 = v o 2 + 2 a Δ x.

What are the 5 kinematic formulas? ›

Kinematics Equations and constant acceleration
• ﻿
• Basically, Galileo presented that not only was the acceleration down a ramp due to gravity constant, but that the velocity increased linearly with time. ...
• or Δx = vavgΔt.
• or vf = vo + aΔt or Δv= aΔt.
• Δx = vo Δt + ½ a Δt2

How is robot reach calculated? ›

Robot reach is the distance from the center of the robot to the fullest extension of the robotic arm. This measurement determines the robot's work envelope.

What are the 3 types of simulation? ›

Simulation systems include discrete event simulation, process simulation and dynamic simulation.

Which is the most common form of dynamic simulation? ›

The article introduced three dynamic simulation modeling methods most commonly used—system dynamics (SD), discrete-event simulation (DES), and agent-based modeling (ABM)—and reviewed where they differ from models more typically used in economic evaluation such as Markov models and decision trees.

What is dynamical method? ›

The Dynamic Method is an approach for solving thermodynamic equilibria in single process units (Zinser et al., 2015, 2016b). It can handle chemical and phase equilibria, as well as mixed problems. This approach is based on the solution of a set of ODEs into their steady state.

### What is dynamic load formula? ›

Substituting the stated values into this (dynamic load) formula, F = 150 pounds X ([32-feet + 4-feet]/sec^2/acceleration of gravity [32 feet-per-sec^2]) = 168.75 pounds. The scale would read 150-pounds while at rest on the ground floor and 168.75-pounds during the 4 seconds accelerating upward to 16 feet-per-second.

What is dynamic force formula? ›

1 Dynamic forces Equations of motion. 2 1, Acceleration (rate of change of Velocity) velocity is the vector version of speed, (speed in a straight line) v – u t = a u = initial velocity (in m/s) v= final velocity (in m/s) t = time (in seconds (s)) a = m/s2 Can be rearranged to v = u + at.

What are the 5 main components of robots? ›

The main components of an industrial robot are Manipulators, End Effectors, Feedback devices, Controllers, and Locomotive devices.

What are the 8 main components of robots? ›

8 main Components of Robots
• Actuation: ADVERTISEMENTS: ...
• Motors: The vast majority of robots use electric motors, including bushed and brushies DC motors.
• Stepper motors: ADVERTISEMENTS: ...
• Piezo Motors: ...
• Air Muscles: ...
• Electroactive polymers: ...
• Elastic Nanotubes: ...
• Manipulation:

What are the 3 main challenges in robotics? ›

Three challenges focus on fundamental problems in robotics: developing robot swarms, improving navigation and exploration, and developing artificial intelligence that can “learn how to learn”, and use common sense to make moral and social decisions.

Who is the father of robotics? ›

Al-Jazari is not only known as the "father of robotics" he also documented 50 mechanical inventions (along with construction drawings) and is considered to be the "father of modern day engineering." The inventions he mentions in his book include the crank mechanism, connecting rod, programmable automaton, humanoid ...

What is the most important part of a robot? ›

One of the main components of a robot is found in any computer-driven technology: the central processing unit (CPU). The CPU acts as the “brain” of the robot. In other words, a CPU is the robot component that provides feedback to outside stimuli. All organisms function and survive by using feedback.

What are the main concepts of a robot? ›

Robotics deals with the design, construction, operation, and use of robots and computer systems for their control, sensory feedback, and information processing. A robot is a unit that implements this interaction with the physical world based on sensors, actuators, and information processing.

What are the 4 types of programming? ›

Functional Programming Language. Scripting Programming Language. Logic Programming Language. Object-Oriented Programming Language.

What is the most suitable method of programming your recommended type of robot? ›

Python is a powerful programming language that may be used to create and test robots. In terms of automation and post-process robotic programming, it outperforms other platforms. You may use this to build a script that will compute, record, and activate a robot code. It is not necessary to teach anything by hand.

### Which programming is best for robotics? ›

The C/C++ language is one of the most widely used programming languages in robotics. The Arduino microcontroller uses a programming language based on C and is a great way to learn the basics of this important language whilst doing hands-on robotics.

What is the most useful algorithm? ›

Boolean (binary) algebra was the foundation of the Information Age. Its impact/implications on the world: This algorithm is widely recognized as the foundation of modern computer coding. It is still in use today, especially in computer circuitry.

What are methods of algorithms? ›

In the following section are descriptions of the main features of two methods of algorithm description: pseudocode and flowcharts. Descriptions and specific examples of the programming structures of sequence, selection, repetition and subprograms (procedures or subroutines) are given.

What are 5 different types of robots? ›

The six most common types of robots are autonomous mobile robots (AMRs), automated guided vehicles (AGVs), articulated robots, humanoids, cobots, and hybrids.

What are 2 basic aspects of robotics? ›

Answer: Robotics deals with the design, construction, operation, and use of robots and computer systems for their control, sensory feedback, and information processing. A robot is a unit that implements this interaction with the physical world based on sensors, actuators, and information processing.

What tools are used in robotics? ›

Mechanical Tool
• Small vise: you'll need not need this.
• Hammer: A hammer is one of the standard tools you'll need.
• Screwdrivers & Wrenches: their uses are obvious. ...
• Saw: Metal and wood saws. ...
• Square, measuring tape, scribe and other marking out tools.
• Vernier calipers: Allow very accurate marking out and measurement.

What are the 3 kinematic formulas? ›

The three equations are, v = u + at. v² = u² + 2as. s = ut + ½at²

What are the 4 basic quantities of kinematics? ›

Kinematics analyzes the positions and motions of objects as a function of time, without regard to the causes of motion. It involves the relationships between the quantities displacement (d), velocity (v), acceleration (a), and time (t).

What are the 5 variables of kinematics? ›

In kinematics there are five important quantities: displacement (change in position), initial velocity, final velocity, acceleration, and time. Initial velocity is how fast an object is moving at t = 0.

What are three examples of dynamic systems? ›

Examples of dynamical systems include population growth, a swinging pendulum, the motions of celestial bodies, and the behavior of “rational” individuals playing a negotiation game, to name a few. The first three examples sound legitimate, as those are systems that typically appear in physics textbooks.

### Which diagram is used for dynamic modelling? ›

Dynamic model is represented graphically with the help of state diagrams. It is also known as state modelling. State model consist of multiple state diagrams, one for each class with temporal behavior that is important to an application. State diagram relates with events and states.

What are dynamic modelling tools? ›

Dynamic Modeling Tools are tools that you use in your classroom to get the students excited about what they are learning. They help students identify relationships and see cause and effect. These tools make lessons in the classroom interactive and more fun for the students.

Why do we use forward kinematics? ›

In forward kinematics our goal is to determine the coordinate of the end effector (and orientation) for given links angles ( and of course lengths); on other hand, in the inverse kinematics we have the coordinate of the end effector (and orientation) and we need to know, what the different angles between links.

What is the use of forward kinematics? ›

1 Forward Kinematics. Forward kinematics refers to process of obtaining position and velocity of end effector, given the known joint angles and angular velocities. For example, if shoulder and elbow joint angles are given for arm in sagittal plane, the goal is to find Cartesian coordinates of wrist/fist.

Why is forward kinematics important? ›

According to the given joint angle or displacement, the robot's forward kinematics should be defined for the position of the robot end effector. It is the basis for further research on robots and it is important for robot workspace analysis, trajectory planning, motion control, and error compensation.

What is forward dynamics and inverse dynamics? ›

The problem of reconstructing the internal forces and/or torques from the movements and known external forces is called the 'inverse dynamics problem', whereas calculating motion from known internal forces and/or torques and resulting reaction forces is called the 'forward dynamics problem'.

What is forward and reverse kinematics in robotics? ›

Forward kinematics is the process of determining the position and orientation of the end effector in Cartesian space with the help of the joint angles [10]. Inverse kinematics is the process of calculating the joint angles with the help of the position and orientation of the end-effector.

What is the difference between forward and inverse kinematics in robotics? ›

Forward kinematics uses the joint parameters to compute the configuration of the chain, and inverse kinematics reverses this calculation to determine the joint parameters that achieve a desired configuration.

What is forward and inverse kinematics of robot manipulator? ›

Forward kinematics asks where the end effector of the arm will be following a sequence of rotations of the joints of the arm. Inverse kinematics asks what rotations of the joints will bring the end effector to a specified position.

What is forward kinematics equation? ›

Forward kinematics refers to the use of the kinematic equations of a robot to compute the position of the end-effector from specified values for the joint parameters.

### Why do we use forward kinematics? ›

In forward kinematics our goal is to determine the coordinate of the end effector (and orientation) for given links angles ( and of course lengths); on other hand, in the inverse kinematics we have the coordinate of the end effector (and orientation) and we need to know, what the different angles between links.

Why is forward kinematics important? ›

According to the given joint angle or displacement, the robot's forward kinematics should be defined for the position of the robot end effector. It is the basis for further research on robots and it is important for robot workspace analysis, trajectory planning, motion control, and error compensation.

Which are the robot programming methods? ›

Robot Programming Methods
• Teach Method. This is by far the most popular standard method of programming a robot. ...
• Joint Co-ordinates. The robot joints are driven independently of each other in the required direction. ...
• Global Co-ordinates. ...
• Tool Co-ordinates. ...
• Workpiece Co-ordinates. ...
• Lead Through. ...
• Off-line Programming.

What are the three types of kinematics? ›

There are three basic concepts in kinematics - speed, velocity and acceleration.

How many solutions does forward kinematics have? ›

As a result, the forward kinematics problem of this manipulator has at most eight real solutions. Based on the solutions, the configurations of the manipulator, including position and orientation of the end-effector, are graphically displayed in Figure 7.

Why is inverse kinematics harder than forward kinematics? ›

It is difficult to solve the inverse kinematics problem because they provide an infinite number of joint motions for a certain end-effector position and orientation [133].

What are the 4 DH parameters? ›

The four D-H parameters: the length of link i (a i ), the angle between the joint axes z i−1 and z i (α i ), the distance between o i−1 and o i along z i (d i ) and the angle between x i−1 and x i (θ i ).

What are the different methods to solve the inverse kinematics? ›

There are two distinct methods of solving inverse kinematics, analytical and iterative. The iterative method gives the solution by solving an approximation of the system, and by updating the system with the output from the solver each iteration until it converges. The analytical method solves the whole system at once.

Is direct kinematics the same as forward kinematics? ›

In the direct kinematics, also called forward kinematics, we define the position of the end-effector as a matrix which is a function of the angles or slides at each joint.

How does a robot move forward? ›

Typically, in order to move their segments in two directions, robots use pistons that can push both ways. The robot's computer controls everything attached to the circuits. To move the robot, the computer switches on all the necessary motors and valves.

### What is forward kinematics problem for a robotic arm? ›

The forward kinematics problem involves finding the end-tip position of a manipulator in a coordinate space given its joint parameters (i.e., joint angles for revolute joints and link offset for prismatic joints). This means that given a certain pose of a robotic arm, the xyz coordinates of the hand must be determined.

## Videos

1. Anqi Li: Safe and Efficient Robot Learning Using Riemannian Motion Policies
(RSS Workshop on Geometry and Topology in Robotics)
2. Modern Robotics, Chapter 8.3: Newton-Euler Inverse Dynamics
(Northwestern Robotics)
3. Dynamics of Robotic Manipulators - Part 1
(Ali Raza)
4. Daniel Bruder on Making Soft Robotics Less Hard | Toronto AIR Seminar
(AI in Robotics Seminar Series)
5. Autonomy Talks - Stephen James: Sample-Efficient Robot Learning
(ETH Zürich Frazzoli)
6. Forward and Inverse Kinematics for ABB IRB-140 Industrial Robot Arms (Remasterized Sound)
(Mechatronics - baqumau)
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