Miroslaw Galicki

Learning continuous trajectories in recurrent neural networks with time-dependent weights

This paper is concerned with a general learning (with arbitrary criterion and state-dependent constraints) of continuous trajectories by means of recurrent neural networks with time-varying weights. The learning process is transformed into an optimal control framework, where the weights to be found are treated as controls. A new learning algorithm based on a variational formulation of Pontryagins maximum principle is proposed. This algorithm is shown to converge, under reasonable conditions, to an optimal solution. The neural networks with time-dependent weights make it possible to efficiently find an admissible solution (i.e., initial weights satisfying state constraints) which then serves as an initial guess to carry out a proper minimization of a given criterion. The proposed methodology may be directly applicable to both classification of temporal sequences and to optimal tracking of nonlinear dynamic systems. Numerical examples are also given which demonstrate the efficiency of the approach presented.

Time-optimal controls of kinematically redundant manipulators with geometric constraints

Theoretical investigations of time-optimal control of kinematically redundant manipulators subject to control and state constraints are presented. The task is to move the end-effector along a prescribed geometric path (state equality constraints). In order to address a structure of time-optimal control, the concept of a regular trajectory derived in Pontryagin et al. (1961) and the extended state space introduced herein are used. Next, it is proved that if the dynamics of a manipulator are defined by n actuators and m path-constrained equations, where m<n, then at most n-m+1 actuators are saturated, provided that the time-optimal manipulator trajectory is regular with respect to a prescribed geometric path given in the work space. Besides, it is shown that these results are also consistent for a point-to-point time-optimal control problem. A computer example involving a planar redundant manipulator of three revolute kinematic pairs is included which confirms the obtained theoretical results.

Structure optimization of neural networks with the A*-algorithm

A method for the construction of optimal structures for feedforward neural networks is introduced. On the basis of a construction of a graph of network structures and an evaluation value which is assigned to each of them, an heuristic search algorithm can be installed on this graph. The application of the A*-algorithm ensures, in theory, both the optimality of the solution and the optimality of the search. For several examples, a comparison between the new strategy and the well-known cascade-correlation procedure is carried out with respect to the performance of the resulting structures.

Path-constrained control of a redundant manipulator in a task space

Abstract This study addresses the problem of controlling a redundant manipulator with both state and control dependent constraints. The task of the robot is to follow by the end-effector a prescribed geometric path given in the task space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results, carried out for a planar manipulator whose end-effector follows a prescribed geometric path given in a task space, illustrate the trajectory performance of the proposed control scheme.

Training trajectories by continuous recurrent multilayer networks

This paper addresses the problem of training trajectories by means of continuous recurrent neural networks whose feedforward parts are multilayer perceptrons. Such networks can approximate a general nonlinear dynamic system with arbitrary accuracy. The learning process is transformed into an optimal control framework where the weights are the controls to be determined. A training algorithm based upon a variational formulation of Pontryagins maximum principle is proposed for such networks. Computer examples demonstrating the efficiency of the given approach are also presented.

Path following by the end-effector of a redundant manipulator operating in a dynamic environment

This paper addresses the problem of generating at the control-loop level a collision-free trajectory for a redundant manipulator operating in dynamic environments which include moving obstacles. The task of the robot is to follow, by the end-effector, a prescribed geometric path given in the work space. The control constraints resulting from the physical abilities of robot actuators are also taken into account during the robot movement. Provided that a solution to the aforementioned robot task exists, the Lyapunov stability theory is used to derive the control scheme. The numerical simulation results for a planar manipulator whose end-effector follows a prescribed geometric path, given in both an obstacle-free work space and a work space including the moving obstacles, illustrate the trajectory performance of the proposed control scheme.

Adaptive path-constrained control of a robotic manipulator in a task space

This study addresses the problem of adaptive controlling of both a nonredundant and a redundant robotic manipulator with state-dependent constraints. The task of the robot is to follow a prescribed geometric path given in the task space, by the end-effector. The aforementioned robot task has been solved on the basis of the Lyapunov stability theory, which is used to derive the control scheme. A new adaptive Jacobian controller is proposed in the paper for the path following of the robot, with both uncertain kinematics and dynamics. The numerical simulation results carried out for a planar redundant three-DOF (three degrees of freedom) manipulator whose end-effector follows a prescribed geometric path given in a two-dimensional (2D) task space, illustrate the trajectory performance of the proposed control scheme.

The structure of time-optimal controls for kinematically redundant manipulators with end-effector path constraints

Addresses the problem of the structure of time-optimal control of kinematically redundant manipulators along a prescribed geometric path subject to control constraints. Based on the concept of a regular trajectory derived in Pontryagin et al. (1961) and the extended state space introduced herein it is proved that if the dynamics of a manipulator is defined by n actuators and m path-constrained equations, where m<n, then at most n-m+1 actuators are saturated during the time-optimal movement along a prescribed geometric path given in the work space. Besides, it is shown that these results are also valid for a point-to-point time-optimal control problem.

An efficient vector quantizer providing globally optimal solutions

This paper presents a new approach in vector quantization that is designed for clustering or source coding. It incorporates both the capability of fast convergence from a monotonically descending algorithm and provides a globally optimal solution by a random optimization technique. Thus, it benefits from properties of deterministic and stochastic search. Comprehensive experiments demonstrate that the new algorithm actually assimilated the advantages of the both components. It may be therefore regarded as an accelerated global optimization method whose convergence is theoretically proved. According to the complexity of the quantization problem, the convergence rate is shown (numerically) to approach that of a coordinate descent algorithm, which is an iterative updating of a single codevector at a time (generalized Lloyd algorithm GLA, i.e., K-means). The new method is investigated and compared with GLA and a globally operating stochastic relaxation technique. The comparison was made with respect to quality, reliability, and efficiency and applied to four categories of data: an easy to grasp example, patterns derived from the EEG, Gauss-Markov, and image sources.

Inverse-free control of a robotic manipulator in a task space

This paper addresses the control problem in a task space of the redundant and/or non-redundant manipulators with both known and parametric unknown kinematics and dynamics. A computationally simple class of the inverse-free control algorithms is proposed for the end-effector trajectory tracking. These controllers use some suitably constructed non-singular matrix whose inverse estimates the product of the manipulator Jacobian by its transposition. Moreover, by introducing a suitably defined sliding vector and nonlinear errors of the parameters estimation, the new controllers generate bounded and continuous signals. Based on the Lyapunov stability theory, inverse-free control schemes proposed are shown to be asymptotically stable provided that some reasonable assumptions are fulfilled during the manipulator movement. The performance of the proposed control strategies is illustrated through computer simulations for a planar redundant manipulator of three revolute kinematic pairs which accomplishes trajectory tracking by the end-effector in a two-dimensional task space.