Recursive Newton-Euler Research Articles

Dynamic modeling and simulation of a torque-controlled spatial quadruped robot

AbstractEvolution has shown that legged locomotion is most adequate for tasks requiring versatile movement on land, allowing animals to traverse a wide variety of environments ranging from natural terrain to artificial, man-made landscapes with great ease. By employing well-designed control schemes, this ability could be replicated for legged robots, enabling them to be used in critical situations that still pose great danger to human integrity, such as search and rescue missions, inspection of hazardous areas, and even space exploration. This work characterizes the quadruped robot and contact dynamics that will compose our in-house simulator to be used for prototyping locomotion control schemes applied to quadruped robots. The proposed simulator computes the robot dynamics using the Recursive Newton-Euler and Composite-Rigid-Body algorithms with a few modifications to make certain aspects relevant for contact detection and control more easily accessible; furthermore, a compliant contact force method alongside stick-slip friction modeled the contact dynamics. To allow the robot to move, a simple PD-independent joint controller was implemented to track a desired leg trajectory. With the same robot and controller implemented using the MuJoCo simulation software, this work evaluates the proposed simulator by comparing characteristic locomotion signals such as the trunk pose and the ground reaction forces. Results showed similar behavior for both simulators, especially with regard to the contact detection, despite the significantly different contact models. Lastly, final remarks to enhance our simulator’s performance are suggested to be explored in future works.

Dynamic Analysis and Control of Redundant Manipulator for Agricultural Applications in a Virtual Environment

In the development of automated manipulators for fruit and vegetable picking technologies, the challenge of ensuring an efficient, stable, and loss-free picking process has been a complex problem. In such an environment, manipulators require the most efficient and robust control for effective operations. In this paper, a serial 9-DOF redundant manipulator (1P8R) is proposed with various controllers for trajectory tracking problems in agricultural applications. The dynamic analysis of redundant manipulator has been carried out using the Recursive Newton-Euler method. The joint configurations of the robot are determined using optimization techniques for specific Task Space Locations (TSLs) by avoiding obstacles. The process of generating joint trajectories has been implemented by considering the cubic polynomial function. For the task of controlling the robot trajectory tracking in the virtual agricultural environment, different combinations of Proportional (P), Integrative (I), Derivative (D), and Feed-Forward (FF) controllers are employed, and a comparative analysis has been performed among these controllers. To verify the performance of the manipulator, simulations are carried out in a virtual environment using Simulink software. Results show that the robot is able to reach specific TSL accurately with better control and it is found that the implementation of Feed-Forward and PID-CTC controllers has better performance in a complex environment.

Dynamic analysis of a three-fingered deployable metamorphic robotic grasper

This paper selects a three-fingered deployable metamorphic robotic grasper as the studied object and presents a distributed dynamic modeling method for the multi-body system based on the metamorphic mechanism. Considering that the grasper contains two independent motion configurations, dynamic models of them are independently established, and then the final dynamic model of the whole grasper is formed. To further improve the modeling accuracy, it is creatively proposed that irregular links can be seen as rigid connections of multiple regular links, by which the dynamic model for the deployment motion of the grasper is firstly established via the Lagrange equation. For the grasping motion, since the finger of the grasper can be equivalent to a planar 4R serial mechanism, the dynamic models of the base mechanism and the basic module are established by the Lagrange equation to obtain the relationships between the driving forces and the equivalent torques. The whole grasper is then established by the recursive Newton-Euler method to enhance the modeling efficiency. Finally, the effectiveness of the dynamic model is well verified by the dynamic simulation.

Collision Detection of a HEXA Parallel Robot Based on Dynamic Model and a Multi-Dual Depth Camera System.

This paper introduces a Hexa parallel robot and obstacle collision detection method based on dynamic modeling and a computer vision system. The processes to deal with the collision issues refer to collision detection, collision isolation, and collision identification applied to the Hexa robot, respectively, in this paper. Initially, the configuration, kinematic and dynamic characteristics during movement trajectories of the Hexa parallel robot are analyzed to perform the knowledge extraction for the method. Next, a virtual force sensor is presented to estimate the collision detection signal created as a combination of the solution to the inverse dynamics and a low-pass filter. Then, a vision system consisting of dual-depth cameras is designed for obstacle isolation and determining the contact point location at the end-effector, an arm, and a rod of the Hexa robot. Finally, a recursive Newton-Euler algorithm is applied to compute contact forces caused by collision cases with the real-Hexa robot. Based on the experimental results, the force identification is compared to sensor forces for the performance evaluation of the proposed collision detection method.

Automatically Deployable Robust Control of Modular Reconfigurable Robot Manipulators

We propose an automatically deployable robust control scheme for modular reconfigurable robot manipulators, which accounts for noisy velocity measurements, yet it maximizes the tracking performance while avoiding chattering effects. Our proposed control approach automatically adapts to any of the possible robot compositions of given sets of modules. The robust stability is guaranteed by exploiting the use of a recursive Newton-Euler scheme with interval arithmetic computations. Moreover, the robust performance is maximized via an online regulation of the control parameters by analyzing the power spectral density of the commanded torque signal. Being fully automatic, the proposed approach allows for a quick deployment and reconfiguration of modular reconfigurable manipulators. The algorithm is validated via simulations and experiments on a commercially available robot.

Modeling and Simulation of Flexible Spacecrafts Based on Dual Quaternions

This paper proposes a description of flexible spacecrafts’ motion and rotation uniformly with dual quaternions. The dynamic equations are derived by using Lagrange equations. Recursive Newton-Euler (RNE) method is introduced to calculate the nonlinear terms in the equations. The simulation results demonstrate the coupling effects during the actuating speed switch of the solar panel.

Identifying Dynamic Parameters With a Novel Software Design for the M-DOF Collaborative Robot

The primary goal of this project was to develop a general identification method via software that can be applied to collaborative robots. To achieve this, the collaborative ultralight robots Kinova Gen2 and Kuka LWR4+ with seven degrees of freedom (M-DOF) were used. Specifically, the “recursive Newton-Euler” formulation was used to provide a set of parameters that could describe the body structure and to create a general symbolic representation for collaborative robots. For parameter estimation, the least squares method was used. In addition, trajectories generated with random numbers typically do not produce consistent results; thus, verified trajectories were used. To verify trajectories, real robots were simulated with V-Rep before being executed. When untested trajectories are first tested on robots, undesirable results may occur. This method was convenient for parameter estimation and robot health; saves time; and increases the consistency of results. Algorithms were coded in MATLAB and ROS packages via Python. MATLAB, ROS, and V-Rep worked together in the Ubuntu operating system. The identification methods were modeled, implemented, tested, and validated successfully, and the results for both robots are reported in this article.

Numerical Simulation of Inertia Matrix for 6 DoF Industrial Robot

The robot dynamic model is essential for the precision and reliability of robot design, motion control, and simulation. A robot inertia matrix, whose elements are coefficients of joint accelerations within the robot equations of motion, plays an important role in the robot’s control design. During robot motion, elements of the inertia matrix are functions of robot configuration (robot joint positions). To facilitate the development of process models and to make an appropriate selection of motion control algorithms, it is useful to perform numerical simulations of inertia matrix elements for different robot trajectories. In this paper, numerical simulation of inertia matrix is presented for 6 DoF industrial robot with revolute joints for the programmed robot motion. Inertia matrix is obtained from the robot dynamical model developed by using modified recursive Newton-Euler algorithm. Based on the presented simulations, variation of effective inertias and magnitude and variation of cross-coupling effects in the robot inertia matrix are examined.

Trajectory Optimization of Contact-Rich Motions Using Implicit Differential Dynamic Programming

This work presents a Differential Dynamic Programming (DDP) approach for systems characterized by implicit dynamics using sensitivity analysis, such as those modelled via inverse dynamics, variational, and implicit integrators. It leads to a more general formulation of DDP, enabling the use of the faster recursive Newton-Euler inverse dynamics. We leverage the implicit formulation for precise and exact contact modelling in DDP, where we focus on two contributions: (1) contact dynamics at the acceleration level; (2) formulation using an invertible contact model in the forward pass and a closed-form solution in the backward pass to improve the numerical resolution of contacts. The performance of the proposed framework is validated by comparing implicit versus explicit DDP for the swing-up of a double pendulum, and by planning motions for two tasks using a single leg model making multi-body contacts with the environment: standing up from ground, where a priori contact enumeration is challenging, and maintaining balance under an external perturbation.

Enhanced impedance control for an sEMG-based prosthetic using RNE approach

Impedance control has been a major challenge faced by most robotic limbs and arms. One of the ways of enhancing the prosthetic performance is by optimising the kinematic and dynamic systems. Therefore, based on surface electromyography (sEMG) signal, this study implemented the recursive Newton-Euler (RNE) approach to establish an effective control for a prosthetics. The model introduced a primal approach which trains the subject to utilise the prosthetic sEMG data through the use of an operator-machine communal control. Further, the study utilised the estimated kinematics of the prosthetic manipulator to measure the joint torques which is expected to activate the prosthetic robotic arm, while using the active compensation to mask the real dynamics. Finally, the research used several simulations for prosthetic grasping, control and angular velocities to show that with the incorporation of the RNE approach, impedance is efficiently managed while the prosthetic devices are better controlled by the subjects.

Enhanced impedance control for an sEMG-based prosthetic using RNE approach

Impedance control has been a major challenge faced by most robotic limbs and arms. One of the ways of enhancing the prosthetic performance is by optimising the kinematic and dynamic systems. Therefore, based on surface electromyography (sEMG) signal, this study implemented the recursive Newton-Euler (RNE) approach to establish an effective control for a prosthetics. The model introduced a primal approach which trains the subject to utilise the prosthetic sEMG data through the use of an operator-machine communal control. Further, the study utilised the estimated kinematics of the prosthetic manipulator to measure the joint torques which is expected to activate the prosthetic robotic arm, while using the active compensation to mask the real dynamics. Finally, the research used several simulations for prosthetic grasping, control and angular velocities to show that with the incorporation of the RNE approach, impedance is efficiently managed while the prosthetic devices are better controlled by the subjects.

Leader/Follower Force Control of Aerial Manipulators

This article focuses on the modeling and controlling of Unmanned Aerial Manipulators (UAMs) in a leader/follower configuration performing a cooperative manipulation task. Each UAM consists of an Unmanned Aerial Vehicle (UAV) with an attached serial-link robotic manipulator. The Recursive Newton-Euler dynamics formulation is employed to account for the interaction between the UAV and its manipulator. The overall system consists of a couple UAMs with a carrying load. The coupling between these systems is due to the exerted forces by their manipulators through the object characterized by its stiffness matrix. A leader/follower control scheme is employed with a stability-analysis tailored to the UAM-pair. The leader UAM defines the trajectory of the moving object while the follower acts so as to reduce the system’s internal reaction forces. Simulation studies are employed to validate the controller’s performance while comparing the system’s response against that derived from a classical nonlinear tracking controller.

A Recursive Dynamic Modeling and Control for Dual-arm Manipulator With Elastic Joints

A recursive dynamic modeling and control is presented for the dual-arm manipulator with elastic joints carrying a common object. For decoupling the effect of elastic joints, the dynamic modeling approach is based on the classic recursive Newton-Euler method but involves high-order derivatives of motion and force variables. The high-order inverse kinematics which is needed in the motion control is presented firstly. With the classic Recursive Newton-Euler (RNEA) method, two-order dynamic model of the dual-arm robot is established, for decoupling the effect of the elastic joints, the form of four-order dynamic model is presented, meanwhile, combining with the high-order dynamic model of the carried object, the completed Dual-Arm Elastic Joints Newton-Euler Algorithm (DA-EJNEA) is established. Then the feedback linearization method is adopted to the motion control based on the DA-EJNEA. Finally, to verify the effectiveness of the proposed method, feedback linearization method based on the DA-EJNEA and the computed torque method based on the dynamic model with rigid joints are used to control the dual-arm coordinated system respectively, the simulation results illustrate the feedback linearization method based on the DA-EJNEA has an obvious advantage for trajectory tracking of the object in the operation space, it behaves reasonable potentials for the model-based control.

Efficient method for robot forward dynamics computation

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.

Dynamic Identification of the Franka Emika Panda Robot With Retrieval of Feasible Parameters Using Penalty-Based Optimization

In this letter, we address the problem of extracting a feasible set of dynamic parameters characterizing the dynamics of a robot manipulator. We start by identifying through an ordinary least squares approach the dynamic coefficients that linearly parametrize the model. From these, we retrieve a set of feasible link parameters (mass, position of center of mass, inertia) that is fundamental for more realistic dynamic simulations or when implementing in real time robot control laws using recursive NewtonEuler algorithms. The resulting problem is solved by means of an optimization method that incorporates constraints on the physical consistency of the dynamic parameters, including the triangle inequality of the link inertia tensors as well as other user-defined, possibly nonlinear constraints. The approach is developed for the increasingly popular Panda robot by Franka Emika, identifying for the first time its dynamic coefficients, an accurate joint friction model, and a set of feasible dynamic parameters. Validation of the identified dynamic model and of the retrieved feasible parameters is presented for the inverse dynamics problem using, respectively, a Lagrangian approach and Newton-Euler computations.

Wpływ zjawiska tarcia na poziom dyskomfortu pracy operatora żurawia leśnego

A mathematical model of a forest crane that is suitable for dynamics analysis of its operation cycle is presented in this paper. The flexibility of the operator’s seat, drives and supports is taken into account. Joint coordinates are applied to describe the motion of the links together with the homogeneous transformations technique. Lagrange equations of the second order are used when deriving the equations of motions. Joint forces and torques are determined based on recursive Newton-Euler algorithms. These joint forces are then used in the LuGre friction model, which allows to calculate the friction coefficients and friction forces. Numerical analyses performed here show the influence of various friction forces on the vibration level as perceived by the operator of the crane. The level of discomfort is discussed based on standards commonly used in the vehicle and transportation industry for evaluations of vibration comfort

Dynamic Modeling and Control for a Deployable Grasping Manipulator

This paper presents a special type of truss-shaped deployable grasping manipulator (DGM) that is suitable for grasping the large-scale objects, but its dynamic modeling is a challenging task because of its multiple closed-loop structures. To address this issue, an iterative dynamic modeling approach is proposed. First, the mechanism structure of the DGM is introduced. Second, the kinematics of the basic deployable parallel mechanism unit with scissor-shaped elements is established, and then, its deployment dynamics are modeled based on the Lagrange method. Third, an iterative dynamic modeling approach for the DGM is proposed to realize the real-time computation based on the recursive Newton-Euler method. Then, a controller with the desired feedforward dynamic compensation for the DGM is proposed to improve the control performance in comparison with the one without feedforward. Finally, experiments are completed to verify the proposed controller on a DGM, and experimental results show that the proposed controller is effective.

Modelling and Closed-Loop System Identification of a Quadrotor-Based Aerial Manipulator

This paper presents the modelling and system identification of a quadrotor-based aerial manipulator. The aerial manipulator model is first derived analytically using the Newton-Euler formulation for the quadrotor and Recursive Newton-Euler formulation for the manipulator. The aerial manipulator is then simulated with the quadrotor under Proportional Derivative (PD) control, with the manipulator in motion. The simulation data is then used for system identification of the aerial manipulator. Auto Regressive with eXogenous inputs (ARX) models are obtained from the system identification for linear accelerations and and yaw angular acceleration . For linear acceleration , and pitch and roll angular accelerations and , Auto Regressive Moving Average with eXogenous inputs (ARMAX) models are identified.

Model Identification and Control Design for a Humanoid Robot

In this paper, model identification and adaptive control design are performed on Devanit-Hartenberg model of a humanoid robot. We focus on the modeling of the 6 degree-of-freedom upper limb of the robot using recursive Newton-Euler (RNE) formula for the coordinate frame of each joint. To obtain sufficient excitation for modeling of the robot, the particle swarm optimization method has been employed to optimize the trajectory of each joint, such that satisfied parameter estimation can be obtained. In addition, the estimated inertia parameters are taken as the initial values for the RNE-based adaptive control design to achieve improved tracking performance. Simulation studies have been carried out to verify the result of the identification algorithm and to illustrate the effectiveness of the control design.

Application of the Dahl friction model in the dynamics analysis of grab cranes

The paper presents dynamics analysis of grab cranes. The cranes can be built out of any number of links, however, only selected links have their own drive that is considered in the flexible form. The cranes are mounted to the ground by means of any number of flexible supports. Joint coordinates and homogeneous transformation matrices are used to describe the cranes’ geometry. Equations of motion are derived using Lagrange equations. Friction phenomenon is taken into account in all joints. The joint forces and torques used to calculate friction torques in the revolute joints and friction forces in the prismatic joints are determined using the recursive Newton-Euler algorithm. Models of revolute and prismatic joints are worked out. Friction coefficients are defined using the Dahl friction model. The results of numerical calculations present the influence of friction on the driving torques, force and behaviour of the load.