Second-order and implicit methods in numerical integration improve tracking performance of the closed-loop inverse kinematics algorithm

A general approach to solve the inverse kinematics problem of series manipulators, i.e. finding the required joint motions for the desired end effector motions, is based on the linear approximation of the forward kinematics map and discretization of the continuous problem. Due to the linearization, first velocities are calculated, so numerical integration needs to be done to get the joint variables. This general solution is just a numerical approximation, thus improving the tracking performance of the inverse kinematics algorithm is of great importance. The application of several numerical integration techniques (implicit Euler, explicit trapezoid, implicit trapezoid) is analyzed, and a fix point iteration is given that can be used to calculate implicit solutions. The tracking performance of the spatial inverse positioning problem of a spatial manipulator is analyzed by checking the tracking error in the desired direction (i.e. along the derivative of the desired end effector path) and in the plane perpendicular to the desired direction. The application of the explicit and implicit trapezoid methods yielded much better tracking performance in the directions orthogonal to the desired direction when the end effector had to track a linear path, while the tracking performance in the desired direction was similar for all the methods. Simulations showed that the application of implicit and second-order methods in the numerical integration may greatly improve the tracking performance of the closed-loop inverse kinematics algorithm

A comparison study of the numerical integration methods in the trajectory tracking application of redundant robot manipulators

Differential kinematic has a wide range application area in robot kinematics. The main advantage of the differential kinematic is that it can be easily implemented any kind of mechanisms. In differential kinematic method, Jacobian is used as a mapping operator in the velocity space. The joint velocities are required to be integrated to obtain the pose of the robot manipulator. This integration can be evaluated by using numerical integration methods, since the inverse kinematic equations are highly complex and nonlinear. Thus, the performances of the numerical integration methods affect the trajectory tracking application. This paper compares the performances of numerical integration methods in the trajectory tracking application of redundant robot manipulators. Four different and widely used numerical integration methods are implemented to the trajectory tracking application of the 7-DOF redundant robot manipulator named PA-10 and simulation results are given

Whole-Body MPC for a Dynamically Stable Mobile Manipulator

Autonomous mobile manipulation offers a dual advantage of mobility provided by a mobile platform and dexterity afforded by the manipulator. In this paper, we present a whole-body optimal control framework to jointly solve the problems of manipulation, balancing and interaction as one optimization problem for an inherently unstable robot. The optimization is performed using a Model Predictive Control (MPC) approach; the optimal control problem is transcribed at the end-effector space, treating the position and orientation tasks in the MPC planner, and skillfully planning for end-effector contact forces. The proposed formulation evaluates how the control decisions aimed at end-effector tracking and environment interaction will affect the balance of the system in the future. We showcase the advantages of the proposed MPC approach on the example of a ball-balancing robot with a robotic manipulator and validate our controller in hardware experiments for tasks such as end-effector pose tracking and door opening

Modeling, simulation, and control of soft robots

2019 Fall.Includes bibliographical references.Soft robots are a new type of robot with deformable bodies and muscle-like actuations, which are fundamentally different from traditional robots with rigid links and motor-based actuators. Owing to their elasticity, soft robots outperform rigid ones in safety, maneuverability, and adaptability. With their advantages, many soft robots have been developed for manipulation and locomotion in recent years. However, the current state of soft robotics has significant design and development work, but lags behind in modeling and control due to the complex dynamic behavior of the soft bodies. This complexity prevents a unified dynamics model that captures the dynamic behavior, computationally-efficient algorithms to simulate the dynamics in real-time, and closed-loop control algorithms to accomplish desired dynamic responses. In this thesis, we address the three problems of modeling, simulation, and control of soft robots. For the modeling, we establish a general modeling framework for the dynamics by integrating Cosserat theory with Hamilton's principle. Such a framework can accommodate different actuation methods (e.g., pneumatic, cable-driven, artificial muscles, etc.). To simulate the proposed models, we develop efficient numerical algorithms and implement them in C++ to simulate the dynamics of soft robots in real-time. These algorithms consider qualities of the dynamics that are typically neglected (e.g., numerical damping, group structure). Using the developed numerical algorithms, we investigate the control of soft robots with the goal of achieving real-time and closed-loop control policies. Several control approaches are tested (e.g., model predictive control, reinforcement learning) for a few key tasks: reaching various points in a soft manipulator's workspace and tracking a given trajectory. The results show that model predictive control is possible but is computationally demanding, while reinforcement learning techniques are more computationally effective but require a substantial number of training samples. The modeling, simulation, and control framework developed in this thesis will lay a solid foundation to unleash the potential of soft robots for various applications, such as manipulation and locomotion

An Overview of Kinematic and Calibration Models Using Internal/External Sensors or Constraints to Improve the Behavior of Spatial Parallel Mechanisms

This paper presents an overview of the literature on kinematic and calibration models of parallel mechanisms, the influence of sensors in the mechanism accuracy and parallel mechanisms used as sensors. The most relevant classifications to obtain and solve kinematic models and to identify geometric and non-geometric parameters in the calibration of parallel robots are discussed, examining the advantages and disadvantages of each method, presenting new trends and identifying unsolved problems. This overview tries to answer and show the solutions developed by the most up-to-date research to some of the most frequent questions that appear in the modelling of a parallel mechanism, such as how to measure, the number of sensors and necessary configurations, the type and influence of errors or the number of necessary parameters

Industrial Robotics

This book covers a wide range of topics relating to advanced industrial robotics, sensors and automation technologies. Although being highly technical and complex in nature, the papers presented in this book represent some of the latest cutting edge technologies and advancements in industrial robotics technology. This book covers topics such as networking, properties of manipulators, forward and inverse robot arm kinematics, motion path-planning, machine vision and many other practical topics too numerous to list here. The authors and editor of this book wish to inspire people, especially young ones, to get involved with robotic and mechatronic engineering technology and to develop new and exciting practical applications, perhaps using the ideas and concepts presented herein

Multi-axial real-time hybrid simulation framework for testing nonlinear structure systems with multiple boundary interfaces

Hybrid simulation is a widely accepted laboratory testing approach that partitions a proposed structure into numerical and physical substructures, for a space- and cost-effective testing method. Structural elements that are expected to remain in the linear elastic range are usually modeled numerically, while computationally intractable nonlinear elements are tested physically. The loads and conditions at the boundaries between the numerical and physical substructures are imposed by servo-hydraulic actuators, with the responses measured by load cells and displacement transducers. Traditionally, these actuators impose boundary condition displacements at slow speeds, while damping and inertial components for the physical specimen are numerically calculated. This slow application of the boundary conditions neglects the rate-dependent behavior of the physical specimen. Real-time hybrid simulation (RTHS) is an alternative to slow speed hybrid simulation approach, where the responses of the numerical substructure are calculated and imposed on the physical substructure at real-world natural hazard excitation speeds. Damping, inertia, and rate-dependent material effects are incorporated in the physical substructure as a result of real-time testing. For a general substructure, the boundary interface has six degrees-of-freedom (DOF); therefore, an actuation system that can apply multi-axial loads is required. In these experiments, the boundary conditions at the interface between the physical and numerical substructures are imposed by two or more actuators. Significant dynamic coupling can be present between the actuators in such setups. Kinematic transformations are required for the operation of each actuator to achieve desired boundary conditions. Furthermore, each actuator possesses inherent dynamics that need appropriate compensation to ensure an accurate and stable operation. Most existing RTHS applications to date have involved the substructuring of the reference structures into numerical and physical components at a single interface with a one-DOF boundary condition and force imposed and measured. Multi-DOF boundary conditions have been explored in a few applications; however a general six-DOF stable implementation has never been achieved. A major research gap in the RTHS domain is the development of a multi-axial RTHS framework capable of handling six DOF boundary conditions and forces, as well as the presence of multiple physical specimens and numerical-to-physical interfaces. In this dissertation, a multi-axial real-time hybrid simulation (maRTHS) framework is developed for realistic nonlinear dynamic assessment of structures under natural hazard excitation. The framework is comprised of numerical and physical substructures, actuator-dynamics compensation, and kinematic transformations between Cartesian and actuator/transducer coordinates. The numerical substructure is compiled on a real-time embedded system, comprised of a microcontroller setup, with onboard memory and processing, that computes the response of finite element models of the structural system, which are then communicated with the hardware setup via the input-output peripherals. The physical substructure is composed of a multi-actuator boundary condition box, loadcells, displacement transducers, and one or more physical specimens. The proposed compensation is a model-based strategy based on the linearized identified models of individual actuators. The concepts of the model-based compensation approach are first validated in a shake table study, and then applied to single and multi-axis RTHS developments. The capabilities of the proposed maRTHS framework are demonstrated via the multi-axial load and boundary condition boxes (LBCBs) at the University of Illinois Urbana-Champaign, via two illustrative examples. First, the maRTHS algorithm including the decoupled controller, and kinematic transformation processes are validated. In this study, a moment frame structure is partitioned into numerical beam-column finite element model, and a physical column with an LBCB boundary condition. This experiment is comprised of six DOFs and excitation is only applied in the plane of the moment frame. Next, the maRTHS framework is subjected to a more sophisticated testing environment involving a multi-span curved bridge structure. In this second example, two LBCBs are utilized for testing of two physical piers, and excitation is applied bi-directionally. Results from the illustrative examples are verified against numerical simulations. The results demonstrate the accuracy and promising nature of the proposed state-of-the-art framework for maRTHS for nonlinear dynamic testing of structural systems using multiple boundary points