Study of Motion Control of A Flexible Link

20th century has witnessed massive upsurge in the use of manipulators in several industries especially in space, defense, and medical industries. Among the types of manipulators used, single link manipulators are the most widely used. A single link robotic manipulator is nothing but a link controlled by an actuator to carry out a particular function such as placing a payload from point A to point B. For low power requirements single link manipulators are made up of light weight materials which require flexibility considerations.Flexibility makes the dynamics of the link heavily non-linear which induces vibrations and overshoot. In this project initially the dynamic model of rigid flexible manipulator is explained, then the state space model of the manipulator system is incorporated into MATLAB. The link flexibility is studied by a single beam FEmodel, where expressions for kinetic and potential energyare employed to derive the torqueequation.The 3 flexible link equations are coupled in terms of 3 variables, θ, Ø and v. The tip angle is finally given aslvfor flexible case whereas for the rigid manipulator the tip angle is same as the hub angle θ. Thereforeaccurate computation of v is very important. The joint flexibility is excluded from analysis.Several comparisons were made between the rigid and flexible link for torque requirement. The relation between the trajectory and hub angle is also plotted in a graph.Finally a PD controller taking the errors and its derivative is designed based on the rigid link dynamics

Multi-objective particle swarm optimization for the structural design of concentric tube continuum robots for medical applications

Concentric tube robots belong to the class of continuum robotic systems whose morphology is described by continuous tangent curvature vectors. They are composed of multiple, interacting tubes nested inside one another and are characterized by their inherent flexibility. Concentric tube continuum robots equipped with tools at their distal end have high potential in minimally invasive surgery. Their morphology enables them to reach sites within the body that are inaccessible with commercial tools or that require large incisions. Further, they can be deployed through a tight lumen or follow a nonlinear path. Fundamental research has been the focus during the last years bringing them closer to the operating room. However, there remain challenges that require attention. The structural synthesis of concentric tube continuum robots is one of these challenges, as these types of robots are characterized by their large parameter space. On the one hand, this is advantageous, as they can be deployed in different patients, anatomies, or medical applications. On the other hand, the composition of the tubes and their design is not a straightforward task but one that requires intensive knowledge of anatomy and structural behavior. Prior to the utilization of such robots, the composition of tubes (i.e. the selection of design parameters and application-specific constraints) must be solved to determine a robotic design that is specifically targeted towards an application or patient. Kinematic models that describe the change in morphology and complex motion increase the complexity of this synthesis, as their mathematical description is highly nonlinear. Thus, the state of the art is concerned with the structural design of these types of robots and proposes optimization algorithms to solve for a composition of tubes for a specific patient case or application. However, existing approaches do not consider the overall parameter space, cannot handle the nonlinearity of the model, or multiple objectives that describe most medical applications and tasks. This work aims to solve these fundamental challenges by solving the parameter optimization problem by utilizing a multi-objective optimization algorithm. The main concern of this thesis is the general methodology to solve for patient- and application-specific design of concentric tube continuum robots and presents key parameters, objectives, and constraints. The proposed optimization method is based on evolutionary concepts that can handle multiple objectives, where the set of parameters is represented by a decision vector that can be of variable dimension in multidimensional space. Global optimization algorithms specifically target the constrained search space of concentric tube continuum robots and nonlinear optimization enables to handle the highly nonlinear elasticity modeling. The proposed methodology is then evaluated based on three examples that include cooperative task deployment of two robotic arms, structural stiffness optimization under the consideration of workspace constraints and external forces, and laser-induced thermal therapy in the brain using a concentric tube continuum robot. In summary, the main contributions are 1) the development of an optimization methodology that describes the key parameters, objectives, and constraints of the parameter optimization problem of concentric tube continuum robots, 2) the selection of an appropriate optimization algorithm that can handle the multidimensional search space and diversity of the optimization problem with multiple objectives, and 3) the evaluation of the proposed optimization methodology and structural synthesis based on three real applications

Kinematic Performance Measures and Optimization of Parallel Kinematics Manipulators: A Brief Review

This chapter covers a number of kinematic performance indices that are instrumental in designing parallel kinematics manipulators. These indices can be used selectively based on manipulator requirements and functionality. This would provide the very practical tool for designers to approach their needs in a very comprehensive fashion. Nevertheless, most applications require a more composite set of requirements that makes optimizing performance more challenging. The later part of this chapter will discuss single-objective and multi-objectives optimization that could handle certain performance indices or a combination of them. A brief description of most common techniques in the literature will be provided

Motion Planning of Redundant Manipulator With Variable Joint Velocity Limit Based on Beetle Antennae Search Algorithm

Redundant manipulators play important roles in many industrial and service applications by assisting people fulfill heavy and repetitive jobs. However, redundant manipulators are coupled highly-nonlinear systems which exert difficulty of redundancy resolution computation. Conventional methods such as pseudo-inverse-based approaches obtain the resolved joint angles from joint velocity level, which may bring about more computational cost and may neglect joint velocity limits. In this work, a motion planning method based on beetle antennae search algorithm (BAS) is proposed for motion planning of redundant manipulators with the variable joint velocity limit. Such proposed work does not need to resolve the velocity kinematics equation as the conventional methods do, and the proposed method can directly deal with the forward kinematics equation to resolve the desired joint angles. The simulation and experiment on the five-link planar manipulator and the Kuka industrial manipulator system demonstrate the efficiency of the proposed method for motion planning of redundant manipulator, and reveal the reliable performance of the BAS algorithm as compared with genetic algorithm (GA), particle swarm optimization (PSO), firefly algorithm(FA) and quantum behaved particle swarm algorithm(QPSO) methods

Trajectory Generation for a Multibody Robotic System: Modern Methods Based on Product of Exponentials

This work presents several trajectory generation algorithms for multibody robotic systems based on the Product of Exponentials (PoE) formulation, also known as screw theory. A PoE formulation is first developed to model the kinematics and dynamics of a multibody robotic manipulator (Sawyer Robot) with 7 revolute joints and an end-effector. In the first method, an Inverse Kinematics (IK) algorithm based on the Newton-Raphson iterative method is applied to generate constrained joint-space trajectories corresponding to straight-line and curvilinear motions of the end effector in Cartesian space with finite jerk. The second approach describes Constant Screw Axis (CSA) trajectories which are generated using Machine Learning (ML) and Artificial Neural Networks (ANNs) techniques. The CSA method smooths the trajectory in the Special Euclidean (SE(3)) space. In the third approach, a multi-objective Swarm Intelligence (SI) trajectory generation algorithm is developed, where the IK problem is tackled using a combined SI-PoE ML technique resulting in a joint trajectory that avoids obstacles in the workspace, and satisfies the finite jerk constraint on end-effector while minimizing the torque profiles. The final method is a different approach to solving the IK problem using the Deep Q-Learning (DQN) Reinforcement Learning (RL) algorithm which can generate different joint space trajectories given the Cartesian end-effector path. For all methods above, the Newton-Euler recursive algorithm is implemented to compute the inverse dynamics, which generates the joint torques profiles. The simulated torque profiles are experimentally validated by feeding the generated joint trajectories to the Sawyer robotic arm through the developed Robot Operating System (ROS) - Python environment in the Software Development Kit (SDK) mode. The developed algorithms can be used to generate various trajectories for robotic arms (e.g. spacecraft servicing missions)

Dynamics and control of robotic systems for on-orbit objects manipulation

Multi-body systems (MSs) are assemblies composed of multiple bodies (either rigid or structurally flexible) connected among each other by means of mechanical joints. In many engineering fields (such as aerospace, aeronautics, robotics, machinery, military weapons and bio-mechanics) a large number of systems (e.g. space robots, aircraft, terrestrial vehicles, industrial machinery, launching systems) can be included in this category. The dynamic characteristics and performance of such complex systems need to be accurately and rapidly analyzed and predicted. Taking this engineering background into consideration, a new branch of study, named as Multi-body Systems Dynamics (MSD), emerged in the 1960s and has become an important research and development area in modern mechanics; it mainly addresses the theoretical modeling, numerical analysis, design optimization and control for complex MSs. The research on dynamics modeling and numerical solving techniques for rigid multi-body systems has relatively matured and perfected through the developments over the past half century. However, for many engineering problems, the rigid multi-body system model cannot meet the requirements in terms of precision. It is then necessary to consider the coupling between the large rigid motions of the MS components and their elastic displacements; thus the study of the dynamics of flexible MSs has gained increasing relevance. The flexible MSD involves many theories and methods, such as continuum mechanics, computational mechanics and nonlinear dynamics, thus implying a higher requirement on the theoretical basis. Robotic on-orbit operations for servicing, repairing or de-orbiting existing satellites are among space mission concepts expected to have a relevant role in a close future. In particular, many studies have been focused on removing significant debris objects from their orbit. While mission designs involving tethers, nets, harpoons or glues are among options studied and analyzed by the scientific and industrial community, the debris removal by means of robotic manipulators seems to be the solution with the longest space experience. In fact, robotic manipulators are now a well-established technology in space applications as they are routinely used for handling and assembling large space modules and for reducing human extravehicular activities on the International Space Station. The operations are generally performed in a tele-operated approach, where the slow motion of the robotic manipulator is controlled by specialized operators on board of the space station or at the ground control center. Grasped objects are usually cooperative, meaning they are capable to re-orient themselves or have appropriate mechanisms for engagement with the end-effectors of the manipulator (i.e. its terminal parts). On the other hand, debris removal missions would target objects which are often non-controlled and lacking specific hooking points. Moreover, there would be a distinctive advantage in terms of cost and reliability to conduct this type of mission profile in a fully autonomous manner, as issues like obstacle avoidance could be more easily managed locally than from a far away control center. Space Manipulator Systems (SMSs) are satellites made of a base platform equipped with one or more robotic arms. A SMS is a floating system because its base is not fixed to the ground like in terrestrial manipulators; therefore, the motion of the robotic arms affects the attitude and position of the base platform and vice versa. This reciprocal influence is denoted as "dynamic coupling" and makes the dynamics modeling and motion planning of a space robot much more complicated than those of fixed-base manipulators. Indeed, SMSs are complex systems whose dynamics modeling requires appropriate theoretical and mathematical tools. The growing importance SMSs are acquiring is due to their operational ductility as they are able to perform complicated tasks such as repairing, refueling, re-orbiting spacecraft, assembling articulated space structures and cleaning up the increasing amount of space debris. SMSs have also been employed in several rendezvous and docking missions. They have also been the object of many studies which verified the possibility to extend the operational life of commercial and scientific satellites by using an automated servicing spacecraft dedicated to repair, refuel and/or manage their failures (e.g. DARPA's Orbital Express and JAXA's ETS VII). Furthermore, Active Debris Removal (ADR) via robotic systems is one of the main concerns governments and space agencies have been facing in the last years. As a result, the grasping and post-grasping operations on non-cooperative objects are still open research areas facing many technical challenges: the target object identification by means of passive or active optical techniques, the estimation of its kinematic state, the design of dexterous robotic manipulators and end-effectors, the multi-body dynamics analysis, the selection of approaching and grasping maneuvers and the post-grasping mission planning are the main open research challenges in this field. The missions involving the use of SMSs are usually characterized by the following typical phases: 1. Orbital approach; 2. Rendez-vous; 3. Robotic arm(s) deployment; 4. Pre-grasping; 5. Grasping and post-grasping operations. This thesis project will focus on the last three. The manuscript is structured as follows: Chapter 1 presents the derivation of a multi-body system dynamics equations further developing them to reach their Kane's formulation; Chapter 2 investigates two different approaches (Particle Swarm Optimization and Machine Learning) dealing with a space manipulator deployment maneuver; Chapter 3 addresses the design of a combined Impedance+PD controller capable of accomplishing the pre-grasping phase goals and Chapter 4 is dedicated to the dynamic modeling of the closed-loop kinematic chain formed by the manipulator and the grasped target object and to the synthesis of a Jacobian Transpose+PD controller for a post-grasping docking maneuver. Finally, the concluding remarks summarize the overall thesis contribution

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

Evolutionary algorithms for active vibration control of flexible manipulator

Flexible manipulator systems offer numerous advantages over their rigid counterparts including light weight, faster system response, among others. However, unwanted vibration will occur when flexible manipulator is subjected to disturbances. If the advantages of flexible manipulator are not to be sacrificed, an accurate model and efficient control system must be developed. This thesis presents the development of a Proportional-Integral-Derivative (PID) controller tuning method using evolutionary algorithms (EA) for a single-link flexible manipulator system. Initially, a single link flexible manipulator rig, constrained to move in horizontal direction, was designed and fabricated. The input and output experimental data of the hub angle and endpoint acceleration of the flexible manipulator were acquired. The dynamics of the system was later modeled using a system identification (SI) method utilizing EA with linear auto regressive with exogenous (ARX) model structure. Two novel EAs, Genetic Algorithm with Parameter Exchanger (GAPE) and Particle Swarm Optimization with Explorer (PSOE) have been developed in this study by modifying the original Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithms. These novel algorithms were introduced for the identification of the flexible manipulator system. Their effectiveness was then evaluated in comparison to the original GA and PSO. Results indicated that the identification of the flexible manipulator system using PSOE is better compared to other methods. Next, PID controllers were tuned using EA for the input tracking and the endpoint vibration suppression of the flexible manipulator structure. For rigid motion control of hub angle, an auto-tuned PID controller was implemented. While for vibration suppression of the endpoint, several PID controllers were tuned using GA, GAPE, PSO and PSOE. The results have shown that the conventional auto-tuned PID was effective enough for the input tracking of the rigid motion. However, for end-point vibration suppression, the result showed the superiority of PID-PSOE in comparison to PID-GA, PID-GAPE and PID-PSO. The performance of the best simulated controller was validated experimentally later. Through experimental validation, it was found that the PID-PSOE was capable to suppress the vibration of the single-link flexible manipulator with highest attenuation of 31.3 dB at the first mode of the vibration. The outcomes of this research revealed the effectiveness of the PID controller tuned using PSOE for the endpoint vibration suppression of the flexible manipulator amongst other evolutionary methods