Stability Analysis for Digital PD Control of Flexible Systems

Most robotic applications demand lightweight and high-speed manipulators for considerably reducing the consumed power and achieving high production rates. The two ways for seeking such high-speed arms are; applying advanced control algorithms and/or performing an extensive optimization of the arm structure itself. Therefore, the topology optimization technique is proposed here for obtaining an optimal robot arm design from both structure and control viewpoints. Results of some researches, that have been previously accomplished by size and shape optimization, were encouraging enough to extend and propose this optimization approach. The method of moving asymptotes (MMA) as an optimization algorithm, the finite element analysis (FEA) by ANSYS, and the time-optimal control method are integrated to gain an optimum design capable of attaining the minimum traveling time. The proposed methodology focuses on performing different comparisons between the proposed optimum topological designs and their initial designs for different robot arms’ sizes and materials. It also distinguishes between the proposed optimum design and the previously achieved one by size optimization under the same operational conditions. Therefore, the significance of the proposed technique is emphasized. It shows that the traveling time is reduced by 44.8%, while the previous work only achieved 23.5%. In addition, the mass is reduced to nearly half of its initial value, taking into account the air damping as the real case in all terrestrial applications.

Modern agricultural machinery such as harvesting robotic arms are necessary to optimize the semi-automated agricultural processes to meet the ever-growing food needs of the population of the world. Production of low cost and highly efficient robotic arms are needed to meet the needs of the small-scale growers of underdeveloped countries. In this regard, mechanical design, sensor placement, and object identification are essential to optimize the performance of agricultural robots. This research is conducted to design a fully automated robotic arm for fruit picking in hydroponics system and research farm using machine vision to help the smallholders. For this purpose, a robotic arm with 1.3 m in height is designed using aluminum (18-gauge) and mild steel (MS-16) as fabrication material for the mechanical structure. The prototype design is tested for stress estimation at various payloads using SolidWorks simulations. The proposed robotic arm is based on a four degrees of freedom (4-DoF) design with the gripper having an opening range of 5.5 to 12 cm depending upon the task to handle various objects. The robotic arm is installed on an expandable vertical mobile platform that enables an expanded operational workspace with lower energy consumption. The total weight of the robotic arm is 60 kgs housing a payload capacity ranging between 8 and 10 kgs in accordance with industry-standard load-bearing specifications. The inverse kinematic algorithm using DH-table is computed with an accuracy of up to 95 % and target height of gripper is cross checked by mounting the ultrasonic sensor at the base of robotic arm. The YOLOv8 algorithm is used for object detection using the depth sense camera having angle range of 0.3 m to 3 m with the precision of up to 96 %. The time needed for recognition of fruits and pitching was about 15 s, with a success rate of up to 90 %. This research produces a low-cost and efficient solution for stallholders by developing a fully automated robotic arm for fruit picking. It optimizes agricultural productivity through improved mechanical design, sensor accuracy, and object detection which reduces labor costs by increasing efficiency of semi-automated farming systems. Further research is required to optimize the overall weight of the system and automation of the movement of robotic arm system between the consecutive rows to build a fully autonomous fruit picking operation in hydroponics.

We consider the standard slotted ALOHA system with a finite number of buffered users. Stability analysis of such a system was initiated by Tsybakov and Mikhailov (1979). Since then several bounds on the stability region have been established; however, the exact stability region is known only for the symmetric system and two-user ALOHA. This paper proves necessary and sufficient conditions for stability of the ALOHA system. We accomplish this by means of a novel technique based on three simple observations: applying mathematical induction to a smaller copy of the system, isolating a single queue for which Loynes' stability criteria is adopted, and finally using stochastic dominance to verify the required stationarity assumptions in the Loynes criterion. We also point out that our technique can be used to assess stability regions for other multidimensional systems. We illustrate it by deriving stability regions for buffered systems with conflict resolution algorithms (see also Georgiadis and Szpankowski (1992) for similar approach applied to stability of token-passing rings).

Stability regions of nonlinear dynamical systems may suffer drastic changes as a consequence of parameter variation. These changes are triggered by local or global bifurcations of the vector field. In this chapter, these changes are studied for two types of local bifurcations on the stability boundary: saddle-node bifurcations and Hopf bifurcations on the stability boundary. Local and global characterizations of the stability boundary (the topological boundary of stability region) will be developed at the bifurcation points and the behavior (changes) of stability boundaries and stability regions at these bifurcations will be studied.

Abstract: This paper focuses on the design and analysis of the basic robotic arm for pick and place operation which eliminates the usage of the shop floor area unlike other robotic arms. In industrial sector moving an object from one place to another is done multiple times in the production line as it has to go under several operations to reach to its final stage. Pick and Place robots are the most common robots in the industrial sector. This robot helps to pick an object and place it on the specified location directed by the operator. What are the advantages of a pick and place robot, and where it is applicable? The stress and strain developed in the robotic arm under the applied load. The displacement of the robotic arm is displayed with the maximum displacement position of the arm. Autodesk Fusion 360 tool is used to design the robotic arm and simulate the stress and displacement analysis.

Abstract: The Main technology of this proposed work was to design and fabrication of pick and place robotic arm by 3d-printing technology. The robot arm will be designed with four degree of freedom and programmed to accomplish accurately simple light material pick and place task to assist in the production line in any industry. ARDUNO an open-source computer hardware and software is applied to control robot arm by driving four servo motors to be capable to modify the position wireless control was done by using a Smartphone with android operating system through a Bluetooth module. The robotic arm Working and its performance in execution of pick and place task should be analyzed

In industry 4.0, to increase flexibility of a robotic arm system, high-DOFs (degrees of freedom) robotic arm system is used for different applications. A traditional way of dealing with high-DOFs configuration control is to utilize kinesthetic teaching in Cartesian space by guiding the robot’s end-effector to targets. Usually, the teaching process takes a long time, and the configuration of the robotic arm makes them only workable for specific application needs. This research presents a novel mechanical design of 7-DOFs humanoid robotic arm and an algorithm to generate human-like motions for the anthropometric robotic arm to solve the problem. Because the humanoid robotic arm exists one redundant DOF, in this paper, this extra DOF is utilized to optimize the human-like motion in performing tasks with minimum angle variance, adjusting force transmission with manipulability ellipsoids, and avoiding obstacles in the environment. Finally, a 7-DOFs humanoid robotic arm is designed and used in a task which is typically performed by bartenders, namely, pouring wine into the glass.

Automation systems are generally made upof three main subsystems, namely mechanical, electricaland software. The interactions among these componentsaffect the integrated system in terms of reliability, quality,scalability, and cost. Therefore, it is imperative that thethree components of automation systems are designedconcurrently through an integrated design paradigm.This leads to the need to teach integrated design conceptsto students in programs such as process automation,electrical and computer engineering, and mechanicalengineering. However, due to the time constraint, it isalmost impossible to run full integrated design classprojects. Therefore, instructors have to decide on theparts of the design process that their class projects haveto focus on, and the parts that have to be reviewed for thecompleteness of the integrated design process. In thispaper we present the design and implementation of amicrocontroller based, 3D printable, low cost robotic armsuitable for teaching integrated design. Moreover, thepaper presents how the robotic arm design is used in anintegrated design project of an Industrial Networks andControllers course. Since the focus of this course is theelectrical and software subsystems of the robotic arm,and we do not have enough time to do a full design,students review the design of the robotic arm presented inthis paper and use it to either 3D print the robotic arm orpurchase the mechanical subsystem of the robotic armthat meets the specification.

In the design and operation of complex dynamical systems, it is essential to ensure that all state trajectories of the dynamical system converge to a desired equilibrium within a guaranteed stability region. Yet, for many practical systems---especially in aerospace---this region cannot be determined a priori and is often challenging to compute. One of the most common methods for computing the stability region is to identify a Lyapunov function. A Lyapunov function is a positive function whose time derivative along system trajectories is non-positive, which provides a sufficient condition for stability and characterizes an estimated stability region. However, existing methods of characterizing a stability region via a Lyapunov function often rely on explicit knowledge of the system governing equations. In this work, we present a new physics-informed machine learning method of characterizing an estimated stability region by inferring a Lyapunov function from system trajectory data that treats the dynamical system as a black box and does not require explicit knowledge of the system governing equations. In our presented Lyapunov function Inference method (LyapInf), we propose a quadratic form for the unknown Lyapunov function and fit the unknown quadratic operator to system trajectory data by minimizing the average residual of the Zubov equation, a first-order partial differential equation whose solution yields a Lyapunov function. The inferred quadratic Lyapunov function can then characterize an ellipsoidal estimate of the stability region. Numerical results on benchmark examples demonstrate that our physics-informed stability analysis method successfully characterizes a near-maximal ellipsoid of the system stability region associated with the inferred Lyapunov function without requiring knowledge of the system governing equations.

This paper investigates the feasibility of incorporating a light-weight robotic arm upon an Unmanned Aerial Vehicle (UAV). It concerns on stabilization and adaptability of the UAV during arm operation, exploring alternatives for a light-weight yet durable and feasible arm design, dynamic modelling and feedback control of the arm and integration of the arm with the UAV upon others. Upon consideration of different arm designs, it is decided that the light-weight and shape-memory characteristic of Shape-Memory Alloys (ie. Nitinol) will serve well as the actuation force behind a 2-link arm design. Thermodynamic modelling of the SMA is required to achieve control for its desired strain (and inadvertently the arm's orientation). Motion planning of the arm is achieved through an inverse kinematics algorithm, with positioning feedback provided from sensors on-board whilst operating in consideration for environmental constraints. By considering the UAV and arm as two separate systems, the dynamic equations of motion were derived respectively, with the effects of one on the other being taken into account as a “disturbance” and being compensated accordingly via the onboard controllers.

The paper focuses on design and control of a new anthropomorphic robot arm enabling the torque measurement in each joint to ensure safety while performing tasks of physical interaction with human and environment. When the contact of the arm with an object occurs, local impedance algorithm provides active compliance of corresponding robot arm joint. Thus, the whole structure of the manipulator can safely interact with unstructured environment. A novel variable control strategy was elaborated to increase the robot functionality and to achieve human-like dynamics of interaction. In the paper, we detail the design procedure of 4-DOF robot arm and optical torque sensors. The experimental results of variable joint impedance control show that proposed approach not only provides safe interaction of entire structure of robot arm with a person, but also improves the effectiveness of contact task performance, enables thus to contact with environment in a delicate manner.

In this paper we present a spherical soft robotic arm made from fabric. The inflatable arm has a small mass and is pneumatically actuated. A configuration is employed with only three actuators controlling the two rotational degrees of freedom of a spherical joint. This differs from the commonly employed antagonistic pairs, including four actuators for two degrees of freedom. The fabrication procedure of the lightweight and compliant system is discussed in detail and uses commonly available materials and tools. The capability of the robotic arm to adjust the joint stiffness as a function of the actuator pressures is investigated and characterized for different deflection directions. The static mapping from the actuator pressures to the orientation of the robotic arm is identified from data and the inverse mapping is employed in a position controller. The modeling and controller derivation are performed for three different stiffness levels demonstrating the ability of the spherical robotic arm to change the joint stiffness independently of controlling the position. The position tracking performance is experimentally evaluated by tracking a square trajectory. A comparison of the tracking performance for the different stiffness levels shows that accurate tracking is more challenging for the smallest joint stiffness. A gray-box model capturing the interactions of the two degrees of freedom is used in a learning scheme that is applied for the smallest stiffness level. The learning approach reduces interactions between the two degrees of freedom and demonstrates the control performance achievable with the system developed.

The usage of industrial robots in manufacturing industries has revolutionized the traditional manufacturing process into more diverse and sustainable modern manufacturing processes. This paper presents the design and analysis of a 6-DOF robotic arm, which will perform a highly précised micro friction stir welding process. Friction stir welding is a technology that is constantly evolving. It has played a vital role in connecting metals in numerous sectors since its invention in 1991, and one of the outcomes of its development is micro friction stir welding, which was invented in 2004. There are numerous advantages that a designed robotic arm possesses over other traditional micro friction stir welding machines, which include high precision, sustainability, flexibility, time, and cost-effectiveness, along with a small operation area. The robotic arm is designed in two phases; the first stage is a design of links and revolute joints, respectively, and high-speed motor selection for the end effector to operate at high torques with required precision and accuracy. In the second phase, the designed model was analyzed using ANSYS software. In this phase, the transient and structural analyses are performed to analyze the performance of the robotic arm under various conditions.

In this paper, a smart mobile robotic arm based on gesture control is designed, which is constituted of a remote-control smart car with a robotic arm equipped on the car. The gesture recognition sensor is the Leap Motion module and uses the Processing API function on the PC to locate the position information of both hands in 3D space and convert it into various control data. It uses Bluetooth and the car system to communicate. The car system uses the STM32's NUCLEO-F411RE development board as the controller to analyze and process the gesture data received by Bluetooth accordingly. The left-hand gesture signal was implemented for the movement control of the car, and the right-hand gesture signal is converted into 5 steering gear PWM signals to control the robot arm Elbow and wrist motion and grab. The experimental results show that the car and robot arm can complete the response accurately and quickly, and implement various remote control according to gestures.

In this paper, we concentrate on the design of a new whole-sensitive robot arm enabling torque measurement in each joint by means of developed optical torque sensors. When the contact of arm with an object occurs, local impedance algorithm provides active compliance of corresponding robot arm joint. Thus, the whole structure of the manipulator can safely interact with unstructured environment. The detailed design procedure of the 4-DOF robot arm and optical torque sensors is described in the paper. The gravity compensation algorithm was elaborated and verified by implementation of the local impedance control of a simple two-link arm manipulator