Three-link Robot Research Articles

Expedited surrogate-based quantification of engineering tolerances using a modified polynomial regression

Statistical analysis is frequently used to determine how manufacturing tolerances or operating condition uncertainties affect system performance. Surrogate is one of the accelerating ways in engineering tolerance quantification to analyze uncertainty with an acceptable computational burden rather than costly traditional methods such as Monte Carlo simulation. Compared with more complicated surrogates such as the Gaussian process, or Radial Basis Function (RBF), the Polynomial Regression (PR) provides simpler formulations yet acceptable outcomes. However, PR with the common least-squares method needs to be more accurate and flexible for approximating nonlinear and nonconvex models. In this study, a new approach is proposed to enhance the accuracy and approximation power of PR in dealing with uncertainty quantification in engineering tolerances. For this purpose, first, by computing the differences between training sample points and a reference point (e.g., nominal design), we employ certain linear and exponential basis functions to transform an original variable design into new transformed variables. A second adjustment is made to calculate the bias between the true simulation model and the surrogate’s approximated response. To demonstrate the effectiveness of the proposed PR approach, we provide comparison results between conventional and proposed surrogates employing four practical problems with geometric fabrication tolerances such as three-bar truss design, welded beam design, and trajectory planning of two-link and three-link (two and three degrees of freedom) robot manipulator. The obtained results prove the preference of the proposed approach over conventional PR by improving the approximation accuracy of the model with significantly lower prediction errors.

Control of three-links robot arm based on fuzzy neural Petri nets

Control of three-links robot arm based on fuzzy neural Petri nets

Control of three-links robot arm based on fuzzy neural Petri nets

Control of three-links robot arm based on fuzzy neural Petri nets

Hybrid Force and Motion Control of a Three-Dimensional Flexible Robot Considering Measurement Noises

This work addresses the end-effector trajectory-tracking force and motion control of a three-dimensional three-link robot considering measurement noises. The last two links of the manipulator are considered as structurally flexible. An absolute coordinate approach is used while obtaining the dynamic equations to avoid complex dynamic equations. In this approach, each link is modeled as if there is no connection between the links. Then, joint connections are expressed as constraint equations. After that, these constraint equations are used in dynamic equations to decrease the number of equations. Then, the resulting dynamic equations are transformed into a form which is suitable for controller design. Furthermore, the dynamic equations are divided as pseudostatic equilibrium and deviation equations. The control torques resulting from the pseudostatic equilibrium and the elastic deflections are obtained easily as the solution of algebraic equations. On the other hand, the control torques corresponding to the deviations are obtained without any linearization. Encoders, strain gauges, position sensors and force and moment sensors are required for measurements. Low pass filters are considered for the sensors. For the crossover frequencies of the sensors, low and high values are chosen to observe the filtering effect on the robot output.

Lateral contact yields longitudinal cohesion in active undulatory systems.

Many animals and robots move using undulatory motion of their bodies. When the bodies are in close proximity undulatory motion can lead to novel collective behavior such as gait synchronization, spatial reconfiguration, and clustering. Here we study the role of contact interactions between model undulatory swimmers: three-link robots in experiment and multilink swimmers in simulation. The undulatory gait of each swimmer is generated through a time-dependent sinusoidal-like waveform which has a fixed phase offset, ϕ. By varying the phase relationship between neighboring swimmers we seek to study how contact forces and planar configurations are governed by the phase difference between neighboring swimmers. We find that undulatory actuation in close proximity drives neighboring swimmers into planar equilibrium configurations that depend on the actuation phase difference. We propose a model for stable planar configurations of nearest-neighbor undulatory swimmers which we call the gait compatibility condition, which is the set of planar and phase configurations in which no collisions occur. Robotic experiments with two, three, and four swimmers exhibit good agreement with the compatibility model. To study the contact forces and the time-averaged equilibrium between undulatory systems we perform simulations. To probe the interaction potential between undulatory swimmers we apply a small force to each swimmer longitudinally to separate them from the compatible configuration and we measure their steady-state displacement. These studies reveal that undulatory swimmers in close proximity exhibit attractive longitudinal interaction forces that drive the swimmers from incompatible to compatible configurations. This system of undulatory swimmers provides new insight into active-matter systems which move through body undulation. In addition to the importance of velocity and orientation coherence in active-matter swarms, we demonstrate that undulatory phase coherence is also important for generating stable, cohesive group configurations.

Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised HR Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator

This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function concerning quaternion variables and designs a feedback–feedforward controller as a control system application using such a network. The quaternion neural network is trained in real-time by introducing a feedback error learning framework to the controller. Thus, the quaternion neural network-based controller functions as an adaptive-type controller. The designed controller is applied to the control problem of a three-link robot manipulator, with the control task of making the robot manipulator’s end effector follow a desired trajectory in the Cartesian space. Computational experiments are conducted to investigate the learning capability and the characteristics of the quaternion neural network used in the controller. The experimental results confirm the feasibility of using the derived learning algorithm based on the generalised Hamiltonian–Real calculus to train the quaternion neural network and the availability of such a network for a control systems application.

Proprioceptive feedback design for gait synchronization in collective undulatory robots

The collective movement of animals has long been a source of inspiration for multi-agent swarm robotics. One of the fundamental goals for swarm robotics study is to understand how effective and robust collective behaviors can emerge from simple interaction principles. When animal or robot collectives are in high-density configurations the ability for visual or auditory sensing is diminished and the opportunities for interacting through mechanical contact are enhanced. In this paper, we study how robots that move through lateral body undulation in close proximity are capable of synchronizing their oscillatory gaits through contact interactions between adjacent robots. Critically, gait phase synchronization occurs without the requirement for robot–robot communication, and instead can be engineered as an emergent property of the robot control system. We present a proprioceptive feedback control system that generates collective gait phase synchronization of undulatory robots in experiment and simulation. We first validate this control system using a simple one-dimensional toy model to demonstrate how proprioceptive feedback governs phase synchronization. Simulations and experiments with undulatory three-link robots further demonstrate how phase synchronization can be controlled. Lastly, we demonstrate that robot pairs moving in a confined tunnel can synchronize their movements which leads to faster group locomotion through confined spaces.

H∞ tracking control for nonlinear multivariable systems using wavelet-type TSK fuzzy brain emotional learning with particle swarm optimization

This paper studies the H∞ tracking control for uncertain nonlinear multivariable systems. We propose a control strategy, which combines the adaptive wavelet-type Takagi-Sugeno-Kang (TSK) fuzzy brain emotional learning controller (WTFBELC) and the H∞ robust tracking compensator. As for the adaptive WTFBELC, it is a main controller designed to mimic the ideal controller. The proposed WTFBELC is to obtain much better ability of handling nonlinearities and uncertainties, but the proposed H∞ robust tracking compensator is to compensate the residual error between the adaptive WTFBELC and the ideal controller. Furthermore, the optimal learning rates of the adaptive WTFBELC are searched quickly by using the particle swarm optimization (PSO) algorithm, and the parameter updated laws are derived based on the steepest descent gradient method. The robust tracking performance of this novel control scheme is guaranteed based on Lyapunov stability theory. The mass-spring-damper mechanical system and the three-link robot manipulator, are used to verify the effectiveness of the proposed adaptive PSO-WTFBELC H∞ control scheme.

Dynamic Inchworm Crawling: Performance Analysis and Optimization of a Three-Link Robot

Inchworm crawling allows for both quasistatic and dynamic gaits at a wide range of actuation frequencies. This locomotion mechanism is common in nonskeletal animals and exploited extensively in the bio-inspired field of soft robotics. In this work we develop and simulate the hybrid dynamic crawling of a three-link robot, with passive frictional contacts. We fabricate and experimentally test such robot under periodic inputs of joints’ angles, with good agreement to the theoretical predictions. This allows to comprehend and exploit the effects of inertia in order to find optimal performance in inputs’ parameters. A simple criterion of robustness to uncertainties in friction is proposed. Tuning the inputs according to this criterion improves the robustness of low-frequency actuation, while increasing the frequency allows for gaits with both high advancement velocity and robustness. Finally, the advantages of uneven mass distribution are studied. Time-scaling technique is introduced to shape inputs that achieve similar effect without reassembling the robot. A machine-learning based optimization is applied to these inputs to further improve the robot's performance in traveling distance.

The programmable CPG model based on Matsuoka oscillator and its application to robot locomotion

The central pattern generator (CPG) is an important functional unit in the spinal cord which can produce rhythmic signals to control locomotion. Recently, there has been a growing interest in programmable central pattern generators (PCPG). In this paper, a new PCPG oscillator and a generic PCPG model based on the Matsuoka oscillator are presented. The perturbation method is used to determine the convergence of the generic PCPG model. The sine signal, the mix signal and chaotic signals are provided as inputs to the model, and the simulation results show that the generic PCPG can learn arbitrary periodic signals. In this paper, the generic PCPGs are allocated at each joint of the compass-like and the three-link robots and their outputs are chosen as joint position commands. The simulations show that the generic PCPG can be used to control robot locomotion effectively. The contributions of this paper are as follows: (1) A new PCPG oscillator based on the Matsuoka oscillator is presented as a beneficial enhancement to the PCPG oscillators. (2) A generic PCPG model is built comprising three PCPG oscillators. It can learn any periodic input signal. These findings are a significant contribution to generic PCPG research.

Brachiation Including Aerial Phase by a Three-link Robot with Front-back and Left-right Symmetric Structures

A gibbon moves between branches by brachiation. This is a fast, dynamic movement that uses the torso as a pendulum and utilizes gravity. Among them, brachiation including aerial phases is faster than normal and can catch farther branches. Such brachiation is called ricochetal brachiation. In this paper, in order to realize brachiation including the aerial phase, we make a robot with symmetrical structure, and perform ricochetal brachiation experiments using the real robots. We used the torque time series we made to do normal brachiation. In addition, based on the torque time series, we realized ricochetal brachiation with a real machine.

Mathematical modeling of one type of three-link robot manipulator

Determining the parameters and conditions under which, when the robot manipulators are operating, the set of optimality criteria can be achieved is an urgent task. In this regard, the problem arises of mathematical modeling of the executive system of a manipulation robot. The article discusses manipulators having rotational, translational and rotational kinematic pairs of the fifth class. Three possible kinematic schemes for such manipulators are given. To describe the movement of the manipulation robot, generalized coordinates are introduced that uniquely determine its configuration. The angles of relative rotations and linear relative displacements of the links were taken as generalized coordinates. A Cartesian rectangular coordinate system was associated with each link of the manipulator and with the fixed base. The problem of determining the relative position of the links and their position in the inertial space was solved by converting one coordinate system to another. As a result, the basic kinematic relations were found that determine the position, speed, and acceleration of the centers of mass of the links in a fixed coordinate system for robot manipulators having one translational and two rotational degrees of mobility. Based on these relations, the problem of constructing equations of dynamics in the form of Lagrange equations of the second kind was solved. The advantage of this form of recording is the closed form of expressions that determine the dynamics of the system, which makes it possible to correctly take into account the internal forces acting in the system. For each of the manipulators considered, systems of three second-order nonlinear differential equations were obtained that describe their dynamics. Due to the need to assess the load moment occurring on the control drive shaft, external generalized forces were reduced to the corresponding generalized coordinate.

Tracking and Cooperative Designs of Robot Manipulators Using Adaptive Fixed-Time Fault-Tolerant Constraint Control

At the outset, a nonlinear dynamic system for the generalized robots with input constraint is given to design an adaptive fixed-time fault-tolerant constraint control (AFTFTCC) for trajectory tracking. The proposed AFTFTCC includes a nonlinear filtering tracking error, which can shape the system response. As the operating point is in the neighborhood of the zero nonlinear filtering tracking error, nonlinear filtering gains are increasing to accelerate its tracking ability. The skew-symmetric matrix's condition for the time-derivative of the inertia matrix and Coriolis and centrifugal force matrix is not required. The upper bound of uncertainties is learned to improve system performance. The stabilities of the closed-loop system are verified by the Lyapunov stability theory. Without true force feedback, the cooperative task of multiple robots with multiple arms is also addressed by the proposed AFTFTCC. Finally, two examples, including the trajectory tracking control of planar three-link robot arm and the cooperative control of dual planar three-link robot arms, are employed to validate the effectiveness and robustness of the proposed control.

A Dai–Yuan conjugate gradient algorithm of linear equation constrained optimization approach for optimal robust controller of bipedal robots

In this article, combined rapidly exponential control Lyapunov function with hybrid zero dynamics, a sufficiently descent projected Dai–Yuan approach is proposed, investigated, and analyzed for online solving optimal robust control problems with linear equation constraints of bipedal robots. Moreover, a new approach is developed for designing optimal robust controller. To demonstrate the effectiveness and feasibility of the proposed method, we will conduct numerical simulations on the model of three-link robot with nonlinear, impulsive, and under-actuated dynamics. Numerical results show that the bipedal robot can walk effectively and stability on the ground though the optimal robust controller when the parameters of the hybrid system model are disturbed three times. Furthermore, under the random noise condition, the bipedal robot can walk stably and effectively through online computing the nonlinear optimization problem for optimal robust controller. In addition, some classical control methods are compared with the developed approach in this article, numerical results are reported and analyzed to substantiate the feasibility and superiority of the proposed method for linear equation constrained optimization problem. Last, this article develops a systematic approach on exploiting optimal robust control technique to design hybrid system models for robustly and accurately via online solving linear equation constrained optimization problems.

Hybrid trajectory/force control strategy for the in vivo robot during stomach biopsy

Traditional endoscopy involves limited surgery called biopsy and abdominal cavity exploration. Limitations like reduced dexterity and limited visualization, because of reduced access to the surgical field, limit the surgeon's perception and increases his strain. This results in error while performing surgery. To reduce this deficiency, the involvement of robotic assistance to surgery is one of the greatest milestones crossed so far in the history of medical science. Many researches have been carried out in this particular domain so far, and the research is still in its infancy stage. Several attempts have been made to diminish the limitations in conventional endoscopes used for biopsy, and new design and control strategies have been proposed. This paper presents a hybrid force/trajectory control strategy of such hyper-redundant robot when the robot interacts with the tissues. The force control is of interest here to avoid the damage of healthy tissues when robot interacts with them. To illustrate the methodology, an example of three-link redundant robot has been considered.

Adaptive Control of Walking Robots Based on Virtual Holonomic Constraints: a Simulative Study

Abstract In this paper an adaptive scheme for the dynamic control of underactuated walking robots with impulse effects is proposed and illustrated for the case of a three-link robot with unknown torso mass. The proposed strategy is based on the virtual control technique, where fictitious control inputs and outputs are defined, which allow the design of a fully actuated-like control law; the reference signals for the virtual outputs are chosen as the solutions of a dynamic constraint, on which the fictitious controls are zero. The validity of the proposed method is motivated by Lyapunov arguments and tested by simulations.

INVESTIGATION OF THE THREE-LINK CRAWLING ROBOTS MOVEMENT ON THE NONDETERMINATED SURFACE

Bionic principles of locomotion are the most promising for displacement and transporting equipment under the most difficult conditions. Robots gait based on the changing shape of the robots body and interaction with the surface by body parts, can find application when moving over rough terrain, in a closed space of technological and natural cavities, where the use of wheel-track or walking principle is not possible. In this paper, we propose the design of a three-link crawling robot equipped with two-coordinate active joints. The robot is equipped by supporting elements. Some supporting elements has adjustable friction coefficients, which allows realize various types of movement algorithms of the device. The article presents a mathematical model of a three-link crawling robot, which allows to study the process of robot movement, including case when the coefficients of friction of the surface under the supports are not equal to each other. In practice, the surface will most often have an inhomogeneous nondeterministic structure, which will lead to a deviation in straight-line motion. The paper proposes an algorithm and a diagram of an automatic control system that allows robot to move along a given path despite the indeterminate surface. This is achieved by using additional sensors: a digital electronic compass, an accelerometer, a GPS module. The paper presents the results of computational experiments and the results obtained during the full-scale tests of the prototype of a three-link robot motion. At the end of the article, a comparative analysis of the experimental and theoretical results confirming the adequacy of the developed mathematical model and computational algorithms is presented.

Parameter Optimization Of CPG And Its Application In Robot

The central pattern generator (CPG) has been identified in the spinal cords as responsible for locomotion movements. It is difficult to select the appropriate values of parameters in CPG model. In this paper, the Matsuoka oscillator is selected as the rhythm-generation model and the bat algorithm is chosen to search the parameters of CPG model. The paper shows the details of the parameters optimization and the diagram of the convergence performance. In the paper, the CPG includes the main rhythm-generation neuron and the minor pattern-formation neuron, and Rowat's neural model is chosen as the pattern-formation neuron. Then the CPG model is applied to the three-link biped robot and the result shows that the method of parameter optimization is effective.

Study and Design of Virtual Laboratory in Robotics-Learning

With the development of virtual reality technology, more and more virtual laboratories are used in the fields of education and scientific research. Many famous universities and scientific research institutions at home and abroad have carried out a lot of research on the virtual laboratory, but most of them stay in the design of some simple experiments and the development of specific functions. This paper is expected to focus on using virtual reality technology to embody the teaching process of Robotics. Through the analysis of the theoretical framework and development approach of virtual experimental technology, a general method is developed to build a virtual laboratory in Robotics-Learning. By contrasting the implementation methods of various virtual experiment techniques, the virtual laboratory technology software framework is established. The effectiveness of the proposed method is verified by the establishment of a three-link robot virtual laboratory. Thus, teaching content could be displayed in the virtual world completely. All these can be used either in college education or training to acquire knowledge about robotics and mechanical.

3リンク鉄棒ロボットの遺伝的アルゴリズムを用いた運動制御

3リンク鉄棒ロボットの遺伝的アルゴリズムを用いた運動制御