Lyapunov stability of cable-driven manipulators with synthetic fibre cables regulated by non-linear full-state feedback controller

Robotic manipulators provide advantages in working environments regarding efficiency and safety, which is further increased in the case of elastic joint manipulators, whose mechanical compliance reduces the energy involved in collisions with workers. Cable-driven manipulators are elastic joint manipulators particularly suitable for industrial inspection thanks to the relocation of actuators outside hostile environments, increasing the manipulator payload-to-weight ratio. Recently, synthetic fibre cables are substituting steel cables due to their better-performing mechanical properties, but their visco-elastic behaviour must be compensated in the controller design. The key novelty of this work is using the four elements model, which includes the viscous behaviour, to design a non-linear full-state feedback controller for cable-driven manipulators. Furthermore, the mathematical proof of the closed-loop Lyapunov stability is provided.

Advanced Dynamics Processes Applied to an Articulated Robot

The paper presents the dynamics of a 2R planar articulated robot, developed by two original methods. One is the classical “Lagrangian” adapted by the author, and the second method is absolutely original. The dynamics of the robot are based in both cases on the variation of the inertial forces in the mechanism, or practically on the influence of the masses of the moving elements of the robot. The influence of external loads, weights and the load to be transported is also taken into account. Another original element of the work is the choice of speeds in such a way that they correspond to an optimum necessary for the inverse kinematics imposed on the robot. For this reason, the dynamic operation will be quiet and without large variations or vibrations. If the speeds of the two electric motors (preferably stepper motors) areadapted to those recommended by the author, the controller (PID) used will have a very light load. It is even possible to eliminate it if the adjustment of the two stepper motors (actuators) is performed according to the speeds indicated by the author of the paper. The kinematic motion imposed by the indicated optimal speeds is dynamically and successfully checked by both methods used.

Visual Haptic Feedback for Training of Robotic Suturing

Current surgical robotic systems are teleoperated and do not have force feedback. Considerable practice is required to learn how to use visual input such as tissue deformation upon contact as a substitute for tactile sense. Thus, unnecessarily high forces are observed in novices, prior to specific robotic training, and visual force feedback studies demonstrated reduction of applied forces. Simulation exercises with realistic suturing tasks can provide training outside the operating room. This paper presents contributions to realistic interactive suture simulation for training of suturing and knot-tying tasks commonly used in robotically-assisted surgery. To improve the realism of the simulation, we developed a global coordinate wire model with a new constraint development for the elongation. We demonstrated that a continuous modeling of the contacts avoids instabilities during knot tightening. Visual cues are additionally provided, based on the computation of mechanical forces or constraints, to support learning how to dose the forces. The results are integrated into a powerful system-agnostic simulator, and the comparison with equivalent tasks performed with the da Vinci Xi system confirms its realism.

A Whole-Body Musculoskeletal Model of the Mouse

Neural control of movement cannot be fully understood without careful consideration of interactions between the neural and biomechanical components. Recent advancements in mouse molecular genetics allow for the identification and manipulation of constituent elements underlying the neural control of movement. To complement experimental studies and investigate the mechanisms by which the neural circuitry interacts with the body and the environment, computational studies modeling motor behaviors in mice need to incorporate a model of the mouse musculoskeletal system. Here, we present the first fully articulated musculoskeletal model of the mouse. The mouse skeletal system has been developed from anatomical references and includes the sets of bones in all body compartments, including four limbs, spine, head and tail. Joints between all bones allow for simulation of full 3D mouse kinematics and kinetics. Hindlimb and forelimb musculature has been implemented using Hill-type muscle models. We analyzed the mouse whole-body model and described the moment-arms for different hindlimb and forelimb muscles, the moments applied by these muscles on the joints, and their involvement in limb movements at different limb/body configurations. The model represents a necessary step for the subsequent development of a comprehensive neuro-biomechanical model of freely behaving mice; this will close the loop between the neural control and the physical interactions between the body and the environment.

Control of trotting gait for load-carrying quadruped walking vehicle with eccentric torso

Aiming at the problems of common methods in trotting gait control of a load-carrying quadruped walking vehicle, a control method, combining virtual model and centroidal dynamics, is proposed. The control of the walking vehicle is divided into two parts, meaning the motion control of the vehicle body and the motion control of the swing leg. The virtual model control method is used to work out the accelerations of the vehicle body, while the centroidal dynamics approach is used to obtain the resultant forces acting on the vehicle. Next, quadratic programming is used to distribute the resultant forces to the foot-ends of the supporting legs. Last, combining the Jacobian matrices of supporting legs, the vehicle body’s motion control is achieved. The virtual forces, acting on the swing leg foot-end, are obtained using the virtual model control method. Combining the swing leg’s Jacobian matrix, joint torques of swing leg are worked out. Simulink and Adams are adopted to jointly simulate omnidirectional trotting of the vehicle, under the condition of fixed and shifting position of eccentric weight. The effects of the virtual model and centroidal dynamics control method are compared with that of the virtual model control method. The results show that the errors of roll angle and pitch angle are reduced by 50%, 89% and 50%, 80%, respectively, as derived by virtual model and centroidal dynamic control method, under the two conditions. The proposed control algorithm is proved effective.

Kinematics analysis of a new parallel robotics

A new type of parallel robot ROBO_003 is presented. Its mechanisms, kinematics, and virtual prototype technology are introduced. The research of degrees of freedom (DOF) is based on screw theory, a set of screw is separated as a branch, which named as constrain screw. The type of three DOF gained by counting constrain screw, the moving platform’s frame, and base platform’s frame is set, respectively, a complete kinematic research including closed-form solutions for direct kinematic problem. The 3-D model of ROBO_003 is established using SOLIDWORKS; position and orientation of motion platform can be gained using ADMAS, which is a type of virtual prototype technology. The resultant shows that the structure of ROBO_003 is reasonable, three DOF of motion platform can be operated in a reasonable range, the solutions to the direct kinematics are right, and robot ROBO_003 can be used in many industrial fields. The research of this article provides a basis for the practical application of parallel robotics ROBO_003.

Comprehensive theory of differential kinematics and dynamics towards extensive motion optimization framework

This paper presents a novel unified theoretical framework for differential kinematics and dynamics for the optimization of complex robot motion. By introducing an 18×18 comprehensive motion transformation matrix, the forward differential kinematics and dynamics, including velocity and acceleration, can be written in a simple chain product similar to an ordinary rotational matrix. This formulation enables the analytical computation of derivatives of various physical quantities (e.g. link velocities, link accelerations, or joint torques) with respect to joint coordinates, velocities and accelerations for a robot trajectory in an efficient manner ([Formula: see text], where [Formula: see text] is the number of the robot’s degree of freedom), which is useful for motion optimization. Practical implementation of gradient computation is demonstrated together with simulation results of robot motion optimization to validate the effectiveness of the proposed framework.

OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement

Movement is fundamental to human and animal life, emerging through interaction of complex neural, muscular, and skeletal systems. Study of movement draws from and contributes to diverse fields, including biology, neuroscience, mechanics, and robotics. OpenSim unites methods from these fields to create fast and accurate simulations of movement, enabling two fundamental tasks. First, the software can calculate variables that are difficult to measure experimentally, such as the forces generated by muscles and the stretch and recoil of tendons during movement. Second, OpenSim can predict novel movements from models of motor control, such as kinematic adaptations of human gait during loaded or inclined walking. Changes in musculoskeletal dynamics following surgery or due to human-device interaction can also be simulated; these simulations have played a vital role in several applications, including the design of implantable mechanical devices to improve human grasping in individuals with paralysis. OpenSim is an extensible and user-friendly software package built on decades of knowledge about computational modeling and simulation of biomechanical systems. OpenSim's design enables computational scientists to create new state-of-the-art software tools and empowers others to use these tools in research and clinical applications. OpenSim supports a large and growing community of biomechanics and rehabilitation researchers, facilitating exchange of models and simulations for reproducing and extending discoveries. Examples, tutorials, documentation, and an active user forum support this community. The OpenSim software is covered by the Apache License 2.0, which permits its use for any purpose including both nonprofit and commercial applications. The source code is freely and anonymously accessible on GitHub, where the community is welcomed to make contributions. Platform-specific installers of OpenSim include a GUI and are available on simtk.org.

Solution of the Robot Forward Dynamics Problem by Using a Recursive Procedure Based on the General System Logical Theory

The paper deals with the forward dynamics problem in robotics. The solution of the problem is found on the basis of a new theory, called “general system logical theory.” It uses operators and transformation of operators extensively to study objects and their relations in the real world. The basic notions and operator equations are given. The forward dynamics problem is presented as a diagram, called “elementary logical system.” The diagram unites a set of variables, a set of operators, and a set of relations between the operators. A generic form of a recursive process using the operators and the Lie product is described. The convergence of the process is discussed. Original operator procedures dedicated to the links of the robot are proposed. The wanted solution is found at the limit of the recursive process. An example is given, as well. The result obtained illustrates the ability of the theory to study robotics problems. The forward dynamics problem is solved in a new way and without inversion of the mass matrix of the robot.

The Acceleration Vector of a Rigid Body

This paper explains the relationship between two existing representations of rigid-body acceleration in a 6-D vector: conventional acceleration, which is the concatenation of two 3-D acceleration vectors, and spatial acceleration, which is the time derivative of a 6-D velocity vector. The two are materially different and obey different composition rules. In particular, spatial accelerations behave like true vectors, and conventional accelerations do not. This paper shows that the conventional acceleration of a rigid body is its apparent spatial acceleration in a moving coordinate system. This implies that both vectors describe the same physical phenomenon but in different coordinate systems. It also implies that rigid-body acceleration really is a vector. The paper concludes with some examples showing how 6-D accelerations are used.

Dynamic Analysis of a Manipulator in a Fluid Environment

The computation of the generalized forces produced by a fluid acting on the links of manipulators is considered here. The evaluation of these forces is necessary for the controller of an underwater manipulator (partially or totally immersed). This article presents an approximate method for the computation of buoyancy in local coordinates. The drag forces are computed by numerical integration of the local drag force. Numerical integration is necessary here to achieve a good precision. A new local reference frame is also added on each link to allow an easy description of the geometry of the links. When those computations are included in the dynamic model, a compromise must be made between computation time and precision, because this inclusion may result in doubling or tripling the number of operations to be performed in comparison with a standard dynamic algorithm.

An Efficient Calculation of Flexible Manipulator Inverse Dynamics

This article presents an efficient recursive computation of the in verse dynamics of flexible manipulators. The algorithm is equiva lent to the nonlinear computed torque law offlexible manipulators. The computation method is based on the generalized Newton-Euler model of flexible manipulators and can be considered as a gener alization of the computed torque control algorithm of rigid robots proposed by Luh, Walker, and Paul for executing joint trajectories. The given algorithm is programmed using Mathematica to get au tomatically an efficient customized symbolic model with a reduced number of operations.

Efficient Factorization of the Joint-Space Inertia Matrix for Branched Kinematic Trees

This paper describes new factorization algorithms that exploit branch-induced sparsity in the joint-space inertia matrix (JSIM) of a kinematic tree. It also presents new formulae that show how the cost of calculating and factorizing the JSIM vary with the topology of the tree. These formulae show that the cost of calculating forward dynamics for a branched tree can be considerably less than the cost for an unbranched tree of the same size. Branches can also reduce complexity; some examples are presented of kinematic trees for which the complexity of calculating and factorizing the JSIM are less than O(n2) and O(n3) , respectively. Finally, a cost comparison is made between an O(n) algorithm and an O(n3) algorithm, the latter incorporating one of the new factorization algorithms. It is shown that the O(n3) algorithm is only 15% slower than the O(n) algorithm when applied to a 30-degrees-of-freedom humanoid, but is 2.6 times slower when applied to an equivalent unbranched chain. This is due mainly to the O(n3) algorithm running about 2.2 times faster on the humanoid than on the chain.

A Spatial Operator Algebra for Manipulator Modeling and Control

A recently developed spatial operator algebra for manipu lator modeling, control, and trajectory design is dis cussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high- level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced concep tual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus the transition from an abstract problem formulation and solution to the detailed mechanization of specific algorithms is greatly simplified.

Forward Dynamics, Elimination Methods, and Formulation Stiffness in Robot Simulation

The numerical simulation problem of tree-structured multi body systems, such as robot manipulators, is usually treated as two separate problems: 1) the forward dynamics problem for computing system accelerations, and 2) the numerical integra tion problem for advancing the state in time. The interaction of these two problems can be important, and has led to new conclusions about the overall efficiency of multibody simula tion algorithms (Cloutier, Pai, and Ascher 1995). In particular, the fastest forward dynamics methods are not necessarily the most numerically stable, and in ill-conditioned cases may slow down popular adaptive step-size integration methods. This phenomenon is called formulation stiffness.

In this article, we first unify the derivation of both the com posite rigid-body method (Walker and Orin 1982) and the articulated-body method (Featherstone 1983, 1987) as two elimination methods for solving the same linear system, with the articulated-body method taking advantage of sparsity. Then the numerical instability phenomenon for the composite rigid- body method is explained as a cancellation error that can be avoided, or at least minimized, when using an appropriate version of the articulated-body method. Specifically, we show that a variant of the articulated-body method is better suited to deal with certain types of ill-conditioning than the composite rigid-body method. The unified derivation also clarifies the un derlying linear algebra of forward dynamics algorithms, and is therefore of interest in its own right.

A Perturbation Approach to Robot Calibration

The forward and reverse solutions of a manipulator with six joints are expanded up to second order in the 24 joint param eters. Assuming that the 24 errors of the 24 joint parameters are independent of the setting of the six controllable joint parameters, if suffices to triangulate the six coordinates (three translational, three rotational) of the end-effector and sub tract the ideal position computed from the forward solution of the ideal error-free robot. This provides 24 equations for 24 unknowns. Calibration compensation consists of correcting the six controllable joint parameters by six controllable ad justments so that the effect of the 24 errors is compensated for.

A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 1: Basic Algorithm

This paper presents a recursive, divide-and-conquer algorithm for calculating the forward dynamics of a robot mechanism, or general rigid-body system, on a parallel computer. It features O(log(n)) time complexity on O(n) processors and is the fastest available algorithm for a computer with a large number of processors and low communications costs. It is an exact, noniterative algorithm and is applicable to mechanisms with any joint type and any topology, including branches and kinematic loops. The algorithm works by recursive application of a formula that constructs the articulatedbody equations of motion of an assembly from those of its constituent parts. The inputs to this formula are the equations of motion of two independent subassemblies, plus a description of how they are to be connected, and the output is the equation of motion of the assembly. Starting with a collection of unconnected rigid bodies, the equations of motion of any rigid-body system can be constructed by repeated application of this formula. This paper, being the first in a two-part series, presents an overview of the new algorithm and a detailed description of the simplest case: unbranched kinematic chains. Details of the general case are presented in Part 2.

A Divide-and-Conquer Articulated-Body Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics. Part 2: Trees, Loops, and Accuracy

This paper is the second in a two part series describing a recursive, divide and conquer algorithm for calculating the forward dynamics of a robot mechanism, or a general rigid body system, on a parallel computer. This paper presents the general version of the algorithm. The derivation begins with an algorithm for kinematic trees, which is then extended to closed loop systems. The general algorithm achieves O(log(n)) time complexity on O(n) processors for all kinematic trees and a large subset of closed loop systems.

This paper also presents a more accurate version of the algorithm and the results of some numerical accuracy tests that compare both versions with the standard articulated body algorithm. The tests use rigid body systems containing up to 1024 bodies, and they show that the divide and conquer algorithm is substantially less accurate than the best serial algorithm but still accurate enough to be useful.

Efficient Dynamic Simulation of a Quadruped Using a Decoupled Tree-Structure Approach

Efficient simulation of a dynamically stable, fast-moving quadruped vehicle has been undertaken at The Ohio State University. Individual leg-link inertial properties, espe cially important at high speeds, are incorporated into the simulation. Also incorporated are the ground contact con siderations of compliance, friction, and impulsive impact forces. Basic efficiency is gained by decoupling of the closed-chain system into a tree-structured, open chain through introduction of spring/damper systems at the ground. The ensuing tree-structure dynamics are solved by developing and applying an extended form of the effi cient O(N) open-chain algorithm of Brandl et al. (1986). Additional speedup in the computations is gained through application of multirate integration and parallelization. One second of real-time simulation on a single Intel iPSC/ 2 Hypercube node takes 66.7 s. Use of multirate integra tion improves four-node parallel performance, giving a total speedup factor of more than 3.

A Biomechanical Model of the Scapulothoracic Joint to Accurately Capture Scapular Kinematics during Shoulder Movements

The complexity of shoulder mechanics combined with the movement of skin relative to the scapula makes it difficult to measure shoulder kinematics with sufficient accuracy to distinguish between symptomatic and asymptomatic individuals. Multibody skeletal models can improve motion capture accuracy by reducing the space of possible joint movements, and models are used widely to improve measurement of lower limb kinematics. In this study, we developed a rigid-body model of a scapulothoracic joint to describe the kinematics of the scapula relative to the thorax. This model describes scapular kinematics with four degrees of freedom: 1) elevation and 2) abduction of the scapula on an ellipsoidal thoracic surface, 3) upward rotation of the scapula normal to the thoracic surface, and 4) internal rotation of the scapula to lift the medial border of the scapula off the surface of the thorax. The surface dimensions and joint axes can be customized to match an individual’s anthropometry. We compared the model to “gold standard” bone-pin kinematics collected during three shoulder tasks and found modeled scapular kinematics to be accurate to within 2mm root-mean-squared error for individual bone-pin markers across all markers and movement tasks. As an additional test, we added random and systematic noise to the bone-pin marker data and found that the model reduced kinematic variability due to noise by 65% compared to Euler angles computed without the model. Our scapulothoracic joint model can be used for inverse and forward dynamics analyses and to compute joint reaction loads. The computational performance of the scapulothoracic joint model is well suited for real-time applications; it is freely available for use with OpenSim 3.2, and is customizable and usable with other OpenSim models.

Improved Lighthill fish swimming model for bio-inspired robots: Modeling, computational aspects and experimental comparisons

The best known analytical model of swimming was originally developed by Lighthill and is known as the large amplitude elongated body theory (LAEBT). Recently, this theory has been improved and adapted to robotics through a series of studies ranging from hydrodynamic modeling to mobile multibody system dynamics. This article marks a further step towards the Lighthill theory. The LAEBT is applied to one of the best bio-inspired swimming robots yet built: the AmphiBot III, a modular anguilliform swimming robot. To that end, we apply a Newton–Euler modeling approach and focus our attention on the model of hydrodynamic forces. This model is numerically integrated in real time by using an extension of the Newton–Euler recursive forward dynamics algorithm for manipulators to a robot without a fixed base. Simulations and experiments are compared on undulatory gaits and turning maneuvers for a wide range of parameters. The discrepancies between modeling and reality do not exceed 16% for the swimming speed, while requiring only the one-time calibration of a few hydrodynamic parameters. Since the model can be numerically integrated in real time, it has significantly superior accuracy compared with computational speed ratio, and is, to the best of our knowledge, one of the most accurate models that can be used in real-time. It should provide an interesting tool for the design and control of swimming robots. The approach is presented in a self contained manner, with the concern to help the reader not familiar with fluid dynamics to get insight both into the physics of swimming and the mathematical tools that can help its modeling.

Function approximation technique-based adaptive virtual decomposition control for a serial-chain manipulator

The virtual decomposition control (VDC) is an efficient tool suitable to deal with the full-dynamics-based control problem of complex robots. However, the regressor-based adaptive control used by VDC to control every subsystem and to estimate the unknown parameters demands specific knowledge about the system physics. Therefore, in this paper, we focus on reorganizing the equation of the VDC for a serial chain manipulator using the adaptive function approximation technique (FAT) without needing specific system physics. The dynamic matrices of the dynamic equation of every subsystem (e.g. link and joint) are approximated by orthogonal functions due to the minimum approximation errors produced. The control, the virtual stability of every subsystem and the stability of the entire robotic system are proved in this work. Then the computational complexity of the FAT is compared with the regressor-based approach. Despite the apparent advantage of the FAT in avoiding the regressor matrix, its computational complexity can result in difficulties in the implementation because of the representation of the dynamic matrices of the link subsystem by two large sparse matrices. In effect, the FAT-based adaptive VDC requires further work for improving the representation of the dynamic matrices of the target subsystem. Two case studies are simulated by Matlab/Simulink: a 2-R manipulator and a 6-DOF planar biped robot for verification purposes.

Multibody Graph Transformations and Analysis Part II: Closed-chain constraint embedding

This is the second part of a two-part paper that develops graph theoretic techniques for the topological transformation and analysis of multibody system dynamics. The first part focused on tree systems, and developed systematic and rigorous techniques for the partitioning, aggregation and sub-structuring of multibody dynamics models. This second part, uses the aggregation techniques as the foundation to develop the constraint-embedding technique that enables the transformation of the non-tree system graphs into tree graphs. This enables the application of a large family of analytical and computational techniques for trees to closed-chain systems. This is illustrated through an extension of the low-order articulated-body forward dynamics algorithm for tree systems to closed-chain systems.

Minimal formulation of joint motion for biomechanisms

Biomechanical systems share many properties with mechanically engineered systems, and researchers have successfully employed mechanical engineering simulation software to investigate the mechanical behavior of diverse biological mechanisms, ranging from biomolecules to human joints. Unlike their man-made counterparts, however, biomechanisms rarely exhibit the simple, uncoupled, pure-axial motion that is engineered into mechanical joints such as sliders, pins, and ball-and-socket joints. Current mechanical modeling software based on internal-coordinate multibody dynamics can formulate engineered joints directly in minimal coordinates, but requires additional coordinates restricted by constraints to model more complex motions. This approach can be inefficient, inaccurate, and difficult for biomechanists to customize. Since complex motion is the rule rather than the exception in biomechanisms, the benefits of minimal coordinate modeling are not fully realized in biomedical research. Here we introduce a practical implementation for empirically-defined internal-coordinate joints, which we call "mobilizers." A mobilizer encapsulates the observations, measurement frame, and modeling requirements into a hinge specification of the permissible-motion manifold for a minimal set of internal coordinates. Mobilizers support nonlinear mappings that are mathematically equivalent to constraint manifolds but have the advantages of fewer coordinates, no constraints, and exact representation of the biomechanical motion-space-the benefits long enjoyed for internal-coordinate models of mechanical joints. Hinge matrices within the mobilizer are easily specified by user-supplied functions, and provide a direct means of mapping permissible motion derived from empirical data. We present computational results showing substantial performance and accuracy gains for mobilizers versus equivalent joints implemented with constraints. Examples of mobilizers for joints from human biomechanics and molecular dynamics are given. All methods and examples were implemented in Simbody™-an open source multibody-dynamics solver available at https://Simtk.org.

New approaches to catheter navigation for interventional radiology simulation

For over 20 years, interventional methods have improved the outcomes of patients with cardiovascular disease. However, these procedures require an intricate combination of visual and tactile feedback and extensive training. In this paper, we describe a series of novel approaches that have led to the development of a high-fidelity simulation system for interventional neuroradiology. In particular, we focus on a new approach for real-time deformation of devices such as catheters and guidewires during navigation inside complex vascular networks. This approach combines a real-time incremental Finite Element Model (FEM), an optimization strategy based on substructure decomposition, and a new method for handling collision response in situations where the number of contact points is very large. We also briefly describe other aspects of the simulation system, from patient-specific segmentation to the simulation of contrast agent propagation and fast volume-rendering techniques for generating synthetic X-ray images in real time. Although currently targeted at stroke therapy, our results are applicable to the simulation of any interventional radiology procedure.

An “optimal”k-needle placement strategy and its application to guiding transbronchial needle aspirations

This article addresses the problem of finding an "optimal" strategy for placing k biopsy needles, given a large number of possible initial needle positions. We consider two variations of the problem: (1) Calculate the smallest set of needles necessary to guarantee a successful biopsy; and (2) Given a number k, calculate k needles such that the probability of a successful biopsy is maximized. Note that "needle" is used as shorthand for the parameter vector that specifies the needle placement. Both problems are formulated in terms of two general, NP-hard optimization problems. Our k-needle placement strategy can be considered as "optimal" in the sense that we are able to formulate it as a known NP-hard problem for which it is believed (NP not equal P conjecture) that no efficient algorithm exists that computes the optimal solution. In other words, our strategy is "optimal" with respect to the best approximative algorithm known for the respective NP-hard problem. For the second variation we have implemented an approximative algorithm that is guaranteed to be within a factor of approximately 0.63 of the exact solution. Given a number k, the algorithm calculates k sets of parameters, each set specifying the placement of a needle and the corresponding probability of success. The resulting probabilities show that our approach can provide valuable decision support for the physician in choosing how many needles to place and how to place them.A typical example of a biopsy where the initial needle position is known approximately is a transbronchial needle aspiration (TBNA). We demonstrate how our "optimal" needle placement strategy can be used to achieve sensor-less guidance of TBNA. The basic idea is to use a patient-specific model of the tracheobronchial tree (from CT/MR) and our model for flexible endoscopes to preoperatively estimate the unknown position of the bronchoscope. The result is a set of candidate shapes for the unknown shape of the bronchoscope before needle placement or, in other words, a (large) number of possible initial needle positions. By parameterizing the handling of the bronchoscope, including the insertion of the biopsy needle, we are able to apply our "optimal" strategy. The result is a TBNA protocol that, if executed during the procedure, prescribes how to handle the bronchoscope to maneuver the needle into the target. With the aforementioned endoscope model, we present a new way of modeling long, flexible instruments. The algorithm requires no initialization or preprocessing and calculates the workspace of an instrument based on its insertion depth and a set of internal and external constraints.

Computational requirements for a discrete Kalman filter in robot dynamics algorithms

In standard classical kinematic and dynamic considerations the equations of motion for an n-link manipulator can be obtained as recursive Newton-Euler equations. Another approach to finding the inverse dynamics equations is to formulate the system dynamics and kinematics as a two-point boundary-value problem. The equivalence between these two approaches has been proved in this paper. Solution to the two-point boundary-value problem leads to the forward dynamics equations which are similar to the equations of Kalman filtering and Bryson-Frazier fixed time-interval smoothing. The extensive numerical studies conducted by the author on the new inverse and forward dynamics algorithms derived from the two-point boundary-value problem establish the same level of confidence as exists for current methods. In order to obtain the algorithms with the smallest coefficients of the polynomial of order O(n), the categorization procedure has been implemented in this work.

A unified approach to mathematical modelling of robotic manipulator dynamics

A new method for computer forming of dynamic equations of open-chain mechanical robot configurations is presented. The algorithm used is of a numeric-iterative type, based on mathematical apparatus of screw theory, which has enabled elimination of the unnecessary computations in the process of dynamic model derivation. In addition to conventional kinematic schemes of robotic manipulators, the branched kinematic chains which have recently found their application in the locomotion of robotic mechanisms were also treated. Both the inverse and direct problems of dynamics were addressed. A comparative analysis was carried out of the numerical complexity of various existing algorithms of numeric-iterative type dealing with the problems of spatial active mechanisms dynamics. It has been shown that the proposed method regardless of its generality, approaches by its models complexity symbolic models, which are valid for particular robotic mechanisms only where they achieve a high degree of efficiency.

A Virtual Simulation Environment for Lunar Rover: Framework and Key Technologies

Lunar rover development involves a large amount of validation works in realistic operational conditions, including its mechanical subsystem and on-board software. Real tests require equipped rover platform and a realistic terrain. It is very time consuming and high cost. To improve the development efficiency, a rover simulation environment called RSVE that affords real time capabilities with high fidelity has been developed. It uses fractional Brown motion (fBm) technique and statistical properties to generate lunar surface. Thus, various terrain models for simulation can be generated through changing several parameters. To simulate lunar rover evolving on natural and unstructured surface with high realism, the whole dynamics of the multi-body systems and complex interactions with soft ground is integrated in this environment. An example for path planning algorithm and controlling algorithm testing in this environment is tested. This simulation environment runs on PC or Silicon Graphics.

A Lie-Theoretic Perspective on O(n) Mass Matrix Inversion for Serial Manipulators and Polypeptide Chains

Over the past several decades a number of O(n) methods for forward and inverse dynamics computations have been developed in the multi-body dynamics and robotics literature. A method was developed in 1974 by Fixman for O(n) computation of the mass-matrix determinant for a serial polymer chain consisting of point masses. In other recent papers, we extended this method in order to compute the inverse of the mass matrix for serial chains consisting of point masses. In the present paper, we extend these ideas further and address the case of serial chains composed of rigid-bodies. This requires the use of relatively deep mathematics associated with the rotation group, SO(3), and the special Euclidean group, SE(3), and specifically, it requires that one differentiates functions of Lie-group-valued argument.