Teresa Paula Azevedo-Perdicoúlis

A multi-objective approach for the motion planning of redundant manipulators

Kinematic redundancy occurs when a manipulator possesses more degrees of freedom than those required to execute a given task. Several kinematic techniques for redundant manipulators control the gripper through the pseudo-inverse of the Jacobian, but lead to a kind of chaotic inner motion with unpredictable arm configurations. Such algorithms are not easy to adapt to optimization schemes and, moreover, often there are multiple optimization objectives that can conflict between them. Unlike single optimization, where one attempts to find the best solution, in multi-objective optimization there is no single solution that is optimum with respect to all indices. Therefore, trajectory planning of redundant robots remains an important area of research and more efficient optimization algorithms are needed. This paper presents a new technique to solve the inverse kinematics of redundant manipulators, using a multi-objective genetic algorithm. This scheme combines the closed-loop pseudo-inverse method with a multi-objective genetic algorithm to control the joint positions. Simulations for manipulators with three or four rotational joints, considering the optimization of two objectives in a workspace without and with obstacles are developed. The results reveal that it is possible to choose several solutions from the Pareto optimal front according to the importance of each individual objective.

A fractional approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots through the pseudoinverse control leads to undesirable drift in the joint space. This paper presents a new technique to solve the inverse kinematics problem of redundant manipulators, which uses a fractional differential of order @a to control the joint positions. Two performance measures are defined to examine the strength and weakness of the proposed method. The positional error index measures the precision of the manipulators end-effector at the target position. The repeatability performance index is adopted to evaluate if the joint positions are repetitive when the manipulator execute repetitive trajectories in the operational workspace. Redundant and hyper-redundant planar manipulators reveal that it is possible to choose in a large range of possible values of @a in order to get repetitive trajectories in the joint space.

Linear Quadratic Nash Games on Positive Linear Systems

In this paper two-player Nash differential games, on an infinite time horizon, with two different information structures have been considered: the open loop and the deterministic feedback information structure. The performance indices were assumed to be of quadratic type and the constraint to be a linear positive differential system. As the main result, a convergent Newtonian algorithm to solve the associated algebraic matrix Riccati equation and generalized algebraic matrix Riccati equation in order to obtain stabilizing solutions which are directly related to the existence of a Nash equilibrium, is presented for each information structure. Finally, we discuss a numerical example to illustrate both algorithms presented.

A 2-DAE system gas network model in view to optimisation as a dynamic game

In this paper, we propose to model the optimisation of gas networks as a disturbed LQ game, where each player chooses his strategy according to a modified Nash condition under OL information structure. The dynamics in the network, as well as the coupling conditions, are modelled through a DAE system, and as a consequence a network with loops and nonpipe elements is considered. Conditions for the existence and uniqueness of such an equilibrium are related to the solution of certain Riccati differential equations and a boundary value problem. For simplicity sake, the two-player case is considered. A simple network, where the players are two controllable elements relevant to the network dynamics, is used to illustrate the calculation procedure.

Existence and Uniqueness of Disturbed Open-Loop Nash Equilibria for Affine-Quadratic Differential Games

In this note, we investigate the solution of a disturbed quadratic open loop (OL) Nash game, whose underlying system is an affine differential equation and with a finite time horizon. We derive necessary and sufficient conditions for the existence/uniqueness of the Nash/worst-case equilibrium. The solution is obtained either via solving initial/terminal value problems (IVP/TVP, respectively) in terms of Riccati differential equations or solving an associated boundary value problem (BVP). The motivation for studying the case of the affine dynamics comes from practical applications, namely the optimization of gas networks. As an illustration, we applied the results obtained to a scalar problem and compare the numerical effectiveness between the proposed approach and an usual Scilab BVP solver.

MODELLING ASPECTS OF DESCRIBING A GAS NETWORK THROUGH A DAE SYSTEM

Abstract The aim of this paper is to represent the dynamics, as well as the coupling, of a gas network through a DAE system, with the intention to model the optimisation of the same network as a LQ game with disturbances. The DAE system is formed by the two Kirchhoff Laws and a discretised hyperbolic model which represents the gas transients in the pipeline. We consider a complex network, i.e. a network with loops and nonpipe elements with some of them being controllable. To conclude, the whole modelling process is illustrated by a simple example network.

Modelling a gas pipeline as a repetitive process: controllability, observability and stability

In this paper, the gas dynamics within the pipelines is modelled as a repetitive process with smoothing. Controllability and observability criteria when the system is steered through initial and boundary data, which is achieved by an adequate choice of the homogeneity, are obtained. From the point of view of the technical applications, it seems to make more sense to consider boundary data controls as for instance in the management of high pressure gas networks. Stability criteria suitable computer simulations are also included.

Boundary control of discrete repetitive processes with smoothing: controllability, observability and disturbance attenuation

In this paper, we proffer an explicit representation of solutions for a specific class of linear repetitive processes with smoothing. This representation is used to obtain direct controllability and observability criteria of this same class of discrete time 2-D systems. Not only classical controllability properties are considered, where control of the system is obtained by choosing its inhomogeneity appropriately, but also controllability of the system by steering it through boundary data control. From the point of view of technical applications, for instance in high pressure gas network modelling (see Azevedo-Perdicoúlis and Jank in Proceedings of n-DS, international workshop on multidimensional systems, Thessaloniki. 2009), it seems to be more reliable to consider boundary data controls. Therefore, in this paper we emphasise boundary data control properties of the system. A disturbed optimal boundary control problem with a quadratic criterion is also solved.

Evolutionary Trajectory Optimization for Redundant Robots

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms have been investigated in the last years. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms. In this case the trajectory planning is formulated as an optimization problem with constraints.

Iterative Solution of Algebraic Matrix Riccati Equations in Open Loop Nash Games

Abstract In this note we study a fixpoint iteration approach to solve algebraic Riccati equations as they appear in general two player Nash differential games on an infinite time horizon, where the information structure is of open loop type. We obtain conditions for existence and uniqueness of non negative solutions. The performance of the numerical algorithm is shown in an example.