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The inverse kinematics of serial manipulators is a central problem in the automatic control of robot manipulators. The main interest has been in inverse kinematics of a six revolute (6R) jointed manipulator with arbitrary geometry. It has been recently shown that the joints of a general 6R manipulator can orient themselves in 16 different configurations (at most), for a given pose of the end--effector. However, there are no good practical solutions available, which give a level of performance expected of industrial manipulators. In this paper, we present an algorithm and implementation for efficient inverse kinematics for a general 6R manipulator. When stated mathematically, the problem reduces to solving a system of multivariate equations. We make use of the algebraic properties of the system and the symbolic formulation used for reducing the problem to solving a univariate polynomial. However, the polynomial is expressed as a matrix determinant and its roots are computed by reducin...

It is well known that in systems described by Euler-Lagrange equations the stability of the equilibria is determined by the potential energy function. Further, these equilibria are asymptotically stable if suitable damping is present in the system. These properties motivated the development of a passivity-based controller design methodology which aims at modifying the potential energy of the closed loop and the addition of the required dissipation. To achieve the latter objective measurement of the generalized velocities is typically required. Our main contribution in this paper is the proof that damping injection without velocity measurement is possible via the inclusion of a dynamic extension provided the system satisfies a dissipation propagation condition. This allows us to determine a class of EulerLagrange systems that can be globally asymptotically stabilized with dynamic output feedback. We illustrate this result with the problem of setpoint control of elastic joints robots. O...

Learning control encompasses a class of control algorithms for programmable machines such as robots which attain, through an iterative process, the motor dexterity that enables the machine to execute complex tasks. In this paper we discuss the use of function identification and adaptive control algorithms in learning controllers for robot manipulators. In particular, we discuss the similarities and differences between betterment learning schemes, repetitive controllers and adaptive learning schemes based on integral transforms. The stability and convergence properties of adaptive learning algorithms based on integral transforms are highlighted and experimental results illustrating some of these properties are presented. Key words: Learning control, adaptive control, repetitive control, robotics. 1 Introduction The emulation of human learning has long been among the most sought after and elusive goals in robotics and artificial intelligence. Many aspects of human learning are still not...

: We present algorithms for 3-D manipulation and conformational analysis of molecular chains, when bond length, bond angles and related dihedral angles remain fixed. These algorithms are useful for local deformations of linear molecules, exact ring closure in cyclic molecules and molecular embedding for short chains. Other possible applications include structure prediction, protein folding, conformation energy analysis and 3D molecular matching and docking. The algorithms are applicable to all serial molecular chains and make no asssumptions about their geometry. We make use of results on direct and inverse kinematics from robotics and mechanics literature and show the correspondence between kinematics and conformational analysis of molecules. In particular, we pose these problems algebraically and compute all the solutions making use of the structure of these equations and matrix computations. The algorithms have been implemented and perform well in practice. In particular, they take ...

: The inverse kinematics of serial manipulators is a central problem in the automatic control of robot manipulators. The main interest has been in inverse kinematics of a six revolute jointed manipulator with arbitrary geometry. It has been recently shown that the joints of a general 6R manipulator can orient themselves in 16 different configurations (at most), for a given pose of the end--effector. However, there are no good practical solutions available, which give a level of performance expected of industrial manipulators. In this paper, we present an algorithm and implementation for real time inverse kinematics for a general 6R manipulator. When stated mathematically, the problem reduces to solving a system of multivariate equations. We make use of the algebraic properties of the system and the techniques used for reducing the problem to solving a univariate polynomial. However, the polynomial is expressed as a matrix determinant and its roots are computed by reducing to an eigenva...

In this thesis, we investigate modeling, control, and coordination of mobile manipulators. A mobile manipulator in this study consists of a robotic manipulator and a mobile platform, with the manipulator being mounted atop the mobile platform. A mobile manipulator combines the dextrous manipulation capability offered by fixed-base manipulators and the mobility offered by mobile platforms. While mobile manipulators offer a tremendous potential for flexible material handling and other tasks, at the same time they bring about a number of challenging issues rather than simply increase the structural complexity. First, combining a manipulator and a platform creates redundancy. Second, a wheeled mobile platform is subject to nonholonomic constraints. Third, there exists dynamic interaction between the manipulator and the mobile platform. Fourth, manipulators and mobile platforms have different bandwidths. Mobile platforms typically have slower dynamic response than manipulators. The objectiv...

We present a framework for analyzing and computing motion plans for a robot that operates in an environment that both varies over time and is not completely predictable. We first classify sources of uncertainty in motion planning into four categories, and argue that the problems addressed in this paper belong to a fundamental category that has received little attention. We treat the changing environment in a flexible manner by combining traditional configuration space concepts with a Markov process that models the environment. For this context, we then propose the use of a motion strategy, which provides a motion command for the robot for each contingency that it could be confronted with. We allow the specification of a desired performance criterion, such as time or distance, and determine a motion strategy that is optimal with respect to that criterion. We demonstrate the breadth of our framework by applying it to a variety of motion planning problems. Examples are computed...

Fuzzy Logic Controllers constitute knowledge-based systems that include Fuzzy Rules and Fuzzy Membership Functions to incorporate human knowledge into their knowledge base. The definition of fuzzy rules and fuzzy membership functions is one of the key question when designing Fuzzy Logic Controllers, and is generally affected by subjective decisions. Some efforts have been made to obtain an improvement on system performance by incorporating learning mechanisms to modify the rules and/or membership functions of the FLC. Genetic Algorithms are probabilistic search and optimization procedures based on natural genetics. This paper proposes a way to apply (with a learning purpose) Genetic Algorithms to Fuzzy Logic Controllers, and presents an application designed to control the Synthesis of biped walk of a simulated 2-D biped robot. KEYWORDS: fuzzy logic control, genetic algorithms, learning Address correspondence to Luis Magdalena, ETS Ingenieros de Telecomunicaci'on, Universidad Polit'ecn...

In this paper we present some ideas on the control of underactuated mechanical systems using switching and saturation. We focus on the swingup control problem for a class of "gymnast" robots and also for the classical cart--pole system. The design methodology is based on partial feedback linearization in a first stage to linearize the actuated degrees of freedom followed by the control of the transfer of energy from the actuated to the unactuated degrees of freedom in a second stage. In a typical swingup control the desired equilibrium is unstable in the closed loop system as a consequence of the non-minimum phase behavior of the system. For this reason it is necessary to switch controllers at the appropriate time to a controller which renders the equilibrium stable. The successful implementation of the switching control has proved to be nontrivial, both in simulation and in experiment. We discuss both local and global design methods and present some simulation results. 1 Introduction ...