Miguel Angel Serna

Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach

A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multi-link flexible robots. The proposed method finds the joint torques necessary to produce a specified end-effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Further more the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solu tion scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested, first through simulation analysis, and second through experimental validation using feed-forward control. Results show the potential use of this method not only for open-loop control, but also for incorporation in feedback control strate gies. 1. This section contains a revised and corrected formulation of open-chain case. A previous method reported by the first author in: Computed Torque for the Fosition Control of Open-Chain Flexible Robots. Proc. 1988 IEEE International Conference in Robotics and Automation contained an error.

A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems

Abstract A modified Lagrangian formulation is presented for the dynamic analysis of constraint mechanisms. The proposed method is based on a Hamiltonian description of the dynamics which leads to the Lagranges equations. However, the constraint conditions are not appended to the Lagranges equations in the form of algebraic or differential constraints, but instead inserted in them by means of a penalty formulation, and therefore the number of equations of the system does not increase. In addition, this approach directly leads to a system of ordinary differential equations, as opposed to the classical Lagranges formulation which results in differential algebraic equations. The resulting set of equations is of the form dot y =g(y,t) , which can be integrated by standard numerical algorithms. Finally, the proposed method is very systematic and general, and can model any type of constraint conditions, either holonomic or nonholonomic. A series of illustrative examples are analyzed. The results demonstrate the capabilities of the proposed method for simulation analysis.

Dynamic analysis of plane mechanisms with lower pairs in basic coordinates

Abstract In this article, we shall present the numerical solution to the dynamic problem of planar mechanisms with lower pairs. This method is based on the basic coordinates and link constraints. We shall begin by describing the matrix formulation of the inertial forces on a link and creating the dynamic equilibrium equations in three different ways: in Lagrangian coordinates, generalized coordinates and coordinates with Lagrange Multipliers. Finally, some examples, obtained by numerical integration of the equations of movement, will be given of problems of evolution in time of the configuration of a mechanical system.

A new representation for collision avoidance and detection

By combining the simplicity of the sphere and the power of the motion of hierarchy of detail, a novel model is proposed with applications to collision avoidance and detection in 3D. The model is based on a double spherical representation for solid bodies. First, each element making up the robot and the obstacles is approximated by a set of exterior spheres which are automatically defined. Second, another set composed of interior spheres is generated. These representations define a hierarchy, since they can be redefined as many times as necessary; starting with two spheres per element, the approximation may be improved until it contains hundreds of spheres. Moreover, they converge to a zero-error representation. The proposed models leads to a simple treatment for the problem of collision detection, and it is further applied to collision-free path planning for manipulators in 3D.<<ETX>>

Spatial Representation and Motion Planning

The spatial representation.- Collision detection.- Motion planning.- Extensions to the model.- Conclusion and future work.

Computer method for kinematic analysis of lower-pair mechanisms—I velocities and accelerations

Abstract This work presents a new method for the analysis of lower pair mechanisms with the help of a computer. This method make use of the coordinates of the pairs and of those of other points of interest as Lagrangian coordinates of the problem. It also makes use of link constraint equations. Perhaps, the most attractive features of this method are its conceptual simplicity and the ease with which it can be programmed in a digital mini-computer. This work is divided into two parts. The first part describes the coordinates and constraint equations made use of, with emphasis on the analysis of velocities and accelerations. The second part presents the resolution of three typically non-linear problems: initial position, finite displacements, and static equilibrium position of a mechanism with elastic connections. It presents an iterative method of rapid convergence and demonstrates that a good initial estimate is not required.

Robicen : a wall-climbing pneumatic robot for inspection in nuclear power plants

Abstract A wall-climbing robot intended for inspection in nuclear power plants has been developed in the context of a cooperative research project which is being carried out by Iberdrola and Nuclenor (Electric Companies), on the one side, and CEIT (Research Centre), on the other. In the first phase of the project, the tasks to be accomplished with the robotic system are of an inspection nature in boiling-water reactor plants. The robot, small in size and modular, is made up of pneumatic components exclusively. Vacuum suction cups are used for sticking the robot to walls to be climbed. The robot motion, made up of both elementary translations and rotations, is accomplished by means of pneumatic cylinders, which constitute the body of the mobile robot. A personal computer is used to command robot motion and a microprocessor controls the electronic valves of all pneumatic components. The paper presents the robotic system conceptual design and gives a detailed description of the mobile robot and its motion.

Inverse dynamics of flexible robots

This paper presents a new and general technique for solving the inverse dynamics of flexible robots. The proposed method finds the joint torques that must be applied by the actuators to obtain a specified end-effector trajectory. Moreover, since the inverse dynamic problem for flexible robots is closely coupled to the inverse kinematic problem, the solution of the inverse dynamics also renders the elastic deformations of the arms and the rotations at the joints. There are no restrictions on the configuration of the flexible robots that can be analyzed with the new technique. Elastic characteristics of the robotic arms are modeled using Euler-Bernoulli beam theory. Lagranges equations, combined with the finite element method to discretize space variables, are used to establish the global dynamic equations of the robot. Kinematic constraints are introduced in the dynamic equations by means of a penalty formulation. Given a tip trajectory, the solution to the posed numerical problem is carried out through a finite differences discretization for the time variable and a collocation procedure that provides the stable, non-causal solution. In contrast with methods previously proposed, this new technique is a non-recursive and non-iterative approach carried out in the time domain. In order to show the performance and accuracy of the proposed method, the paper presents simulation analysis for different robots and several trajectories. When available, the results are compared with those published in previous literature.

Computer method for kinematic analysis of lower-pair mechanisms—II position problems

Abstract In the first part of this study, a new method for solving the problem of kinematic analysis was presented, based on the concepts of “basic coordinates” and “link constraint equations”. In this second part, these same concepts are used to solve the problems of initial position, finite displacements and static equilibrium position of a mechanism with springs between its links. The proposed algorithms are elementary in their formulation and of exceptional efficiency in their performance. The methods describes are based on the solution of a problem of mathematical programming. Several examples are presented, giving an idea of the potential of said algorithms.

Perception-based learning for motion in contact in task planning

This paper presents a new approach to error detection during motion in contact under uncertainty for robotic manufacturing tasks. In this approach, artificial neural networks are used for perception-based learning. The six force-and-torque signals from the wrist sensor of a robot arm are fed into the network. A self-organizing map is what learns the different contact states in an unsupervised way. The method is intended to work properly in complex real-world manufacturing environments, for which existent approaches based on geometric analytical models may not be feasible, or may be too difficult. It is used for different tasks involving motion in contact, particularly the peg-in-hole insertion task, and complex insertion or extraction operations in a flexible manufacturing system. Several real examples for these cases are presented.