Kinematically optimal hyper-redundant manipulator configurations

“Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods

Dynamic Modeling of a Spatial Cable-Driven Continuum Robot Using Euler-Lagrange Method

Continuum robots are kinematically redundant and their dynamic models are highly nonlinear. This study aims to overcome this difficulty by presenting a more practical dynamic model of a certain class of continuum robots called cable-driven continuum robot (CDCR). Firstly, the structural design of a CDCR with two rotational degrees of freedom (DOF) is introduced. Then, the kinematic models are derived according to the constant curvature assumption. Considering the complexity of the kinetic energy expression, it has been approximated by the well-known Taylor expansions.  This case corresponds to weak bending angles within the specified bending angle range of the robot. On the other hand, due to the low weight of the CDCR components, the gravitational energy effects can be neglected compared to those stemmed from the elastic energy. Thereafter, the corresponding dynamic model is established using Euler-Lagrange method. Static and dynamic models have been illustrated by examples. This analysis and dynamic model development have been compared with the existing scientific literature. The obtained results shown that the consistency and the efficiency of accuracy for real-time have been carried out. However, the dynamic modeling of CDCR with more than 2-DOF leads to a more complex mathematical expression, and cannot be simplified by adopting the similar assumptions and methodology used in the case of 2-DOF

Modeling, Control, and Motion Analysis of a Class of Extensible Continuum Manipulators

In this dissertation, the development of a kinematic model, a configuration-space controller, a master-slave teleoperation controller, along with the analysis of the self-motion properties for redundant, extensible, continuous backbone (continuum) ``trunk and tentacle\u27 manipulators are detailed. Unlike conventional rigid-link robots, continuum manipulators are robots that can bend at any point along their backbone, resulting in new and unique modeling and control issues. Taken together, these chapters represent one of the first efforts towards devising model-based controllers of such robots, as well as characterizing their self-motion in its simplest form. Chapter 2 describes the development of a convenient set of generalized, spatial forward kinematics for extensible continuum manipulators based on the robot\u27s measurable variables. This development, takes advantage of the standard constant curvature assumption made for such manipulators and is simpler and more intuitive than the existing kinematic derivations which utilize a pseudo-rigid link manipulator. In Chapter 3, a new control strategy for continuum robots is presented. Control of this emerging new class of robots has proved difficult due to the inherent complexity of their dynamics. Using a recently established full Lagrangian dynamic model, a new nonlinear model-based control strategy (sliding-mode control) for continuum robots is introduced. Simulation results are illustrated using the dynamic model of a three-section, six Degree-of-Freedom, planar continuum robot and an experiment was conducted on the OctArm 9 Degree-of-Freedom continuum manipulator. In both the simulation and experiment, the results of the sliding-mode controller were found to be significantly better than a standard inverse-dynamics PD controller. In Chapter 4, the nature of continuum manipulator self-motion is studied. While use of the redundant continuum manipulator self-motion property (configuration changes which leave the end-effector location fixed) has been proposed, the nature of their null-spaces has not previously been explored. The manipulator related resolved-motion rate inverse kinematics which are based on the forward kinematics described in Chapter 2, are used. Based on these derivations, the self-motion of a 2-section, extensible redundant continuum manipulator in planar and spatial situations (generalizable to n-sections) is analyzed. The existence of a single self-motion manifold underlying the structures is proven, and simple self-motion cases spanning the null-space are introduced. The results of this analysis allow for a better understanding of general continuum robot self-motions and relate their underlying structure to real world examples and applications. The results are supported by experimental validation of the self-motion properties on the 9 Degree-of-Freedom OctArm continuum manipulator. In Chapter 5, teleoperation control of a kinematically redundant, continuum slave robot by a non-redundant, rigid-link master system is described. This problem is novel because the self-motion of the redundant robot can be utilized to achieve secondary control objectives while allowing the user to only control the tip of the slave system. To that end, feedback linearizing controllers are proposed for both the master and slave systems, whose effectiveness is demonstrated using numerical simulations and experimental results (using the 9 Degree-of-Freedom OctArm continuum manipulator as the slave system) for trajectory tracking as well as singularity avoidance subtask

Control Techniques for Robot Manipulator Systems with Modeling Uncertainties

This dissertation describes the design and implementation of various nonlinear control strategies for robot manipulators whose dynamic or kinematic models are uncertain. Chapter 2 describes the development of an adaptive task-space tracking controller for robot manipulators with uncertainty in the kinematic and dynamic models. The controller is developed based on the unit quaternion representation so that singularities associated with the otherwise commonly used three parameter representations are avoided. Experimental results for a planar application of the Barrett whole arm manipulator (WAM) are provided to illustrate the performance of the developed adaptive controller. The controller developed in Chapter 2 requires the assumption that the manipulator models are linearly parameterizable. However there might be scenarios where the structure of the manipulator dynamic model itself is unknown due to difficulty in modeling. One such example is the continuum or hyper-redundant robot manipulator. These manipulators do not have rigid joints, hence, they are difficult to model and this leads to significant challenges in developing high-performance control algorithms. In Chapter 3, a joint level controller for continuum robots is described which utilizes a neural network feedforward component to compensate for dynamic uncertainties. Experimental results are provided to illustrate that the addition of the neural network feedforward component to the controller provides improved tracking performance. While Chapter\u27s 2 and 3 described two different joint controllers for robot manipulators, in Chapter 4 a controller is developed for the specific task of whole arm grasping using a kinematically redundant robot manipulator. The whole arm grasping control problem is broken down into two steps; first, a kinematic level path planner is designed which facilitates the encoding of both the end-effector position as well as the manipulators self-motion positioning information as a desired trajectory for the manipulator joints. Then, the controller described in Chapter 3, which provides asymptotic tracking of the encoded desired joint trajectory in the presence of dynamic uncertainties is utilized. Experimental results using the Barrett Whole Arm Manipulator are presented to demonstrate the validity of the approach

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Modeling, Analysis, Force Sensing and Control of Continuum Robots for Minimally Invasive Surgery

This dissertation describes design, modeling and application of continuum robotics for surgical applications, specifically parallel continuum robots (PCRs) and concentric tube manipulators (CTMs). The introduction of robotics into surgical applications has allowed for a greater degree of precision, less invasive access to more remote surgical sites, and user-intuitive interfaces with enhanced vision systems. The most recent developments have been in the space of continuum robots, whose exible structure create an inherent safety factor when in contact with fragile tissues. The design challenges that exist involve balancing size and strength of the manipulators, controlling the manipulators over long transmission pathways, and incorporating force sensing and feedback from the manipulators to the user. Contributions presented in this work include: (1) prototyping, design, force sensing, and force control investigations of PCRs, and (2) prototyping of a concentric tube manipulator for use in a standard colonoscope. A general kinetostatic model is presented for PCRs along with identification of multiple physical constraints encountered in design and construction. Design considerations and manipulator capabilities are examined in the form of matrix metrics and ellipsoid representations. Finally, force sensing and control are explored and experimental results are provided showing the accuracy of force estimates based on actuation force measurements and control capabilities. An overview of the design requirements, manipulator construction, analysis and experimental results are provided for a CTM used as a tool manipulator in a traditional colonoscope. Currently, tools used in colonoscopic procedures are straight and exit the front of the scope with 1 DOF of operation (jaws of a grasper, tightening of a loop, etc.). This research shows that with a CTM deployed, the dexterity of these tools can be increased dramatically, increasing accuracy of tool operation, ease of use and safety of the overall procedure. The prototype investigated in this work allows for multiple tools to be used during a single procedure. Experimental results show the feasibility and advantages of the newly-designed manipulators

Developing Intuitive, Closed-Loop, Teleoperative Control of Continuum Robotic Systems

This thesis presents a series of related new results in the area of continuum robot teleoperation and control. A new nonlinear control strategy for the teleoperation of extensible continuum robots is described. Previous attempts at controlling continuum robots have proven difficult due to the complexity of their system dynamics. Taking advantage of a previously developed dynamic model for a three-section, planar, continuum manipulator, we present an adaptation control-inspired law. Simulation and experimental results of a teleoperation scheme between a master device and an extensible continuum slave manipulator using the new controller are presented. Two novel user interface approaches to the teleoperation of continuum robots are also presented. In the first, mappings from a six Degree-of-Freedom (DoF) rigid-link robotic arm to a nine degree-of-freedom continuum robot are synthesized, analyzed, and implemented, focusing on their potential for creating an intuitive operational interface. Tests were conducted across a range of planar and spatial tasks, using fifteen participant operators. The results demonstrate the feasibility of the approach, and suggest that it can be effective independent of the prior robotics, gaming, or teleoperative experience of the operator. In the second teleoperation approach, a novel nine degree-of-freedom input device for the teleoperation of extensible continuum robots is introduced. As opposed to previous works limited by kinematically dissimilar master devices or restricted degrees-of-freedom, the device is capable of achieving configurations identical to a three section continuum robot, and simplifying the control of such manipulators. The thesis discusses the design of the control device and its construction. The implementation of the new master device is discussed and the effectiveness of the system is reported

TMTDyn: A Matlab package for modeling and control of hybrid rigid–continuum robots based on discretized lumped systems and reduced-order models

A reliable, accurate, and yet simple dynamic model is important to analyzing, designing, and controlling hybrid rigid–continuum robots. Such models should be fast, as simple as possible, and user-friendly to be widely accepted by the evergrowing robotics research community. In this study, we introduce two new modeling methods for continuum manipulators: a general reduced-order model (ROM) and a discretized model with absolute states and Euler–Bernoulli beam segments (EBA). In addition, a new formulation is presented for a recently introduced discretized model based on Euler–Bernoulli beam segments and relative states (EBR). We implement these models in a Matlab software package, named TMTDyn, to develop a modeling tool for hybrid rigid–continuum systems. The package features a new high-level language (HLL) text-based interface, a CAD-file import module, automatic formation of the system equation of motion (EOM) for different modeling and control tasks, implementing Matlab C-mex functionality for improved performance, and modules for static and linear modal analysis of a hybrid system. The underlying theory and software package are validated for modeling experimental results for (i) dynamics of a continuum appendage, and (ii) general deformation of a fabric sleeve worn by a rigid link pendulum. A comparison shows higher simulation accuracy (8–14% normalized error) and numerical robustness of the ROM model for a system with a small number of states, and computational efficiency of the EBA model with near real-time performances that makes it suitable for large systems. The challenges and necessary modules to further automate the design and analysis of hybrid systems with a large number of states are briefly discussed