Radosław Zawiski

An approach to observability analysis and estimation of human arm model

This article presents the analysis of a mathematical model of human arms dynamics in terms of observability. The research is conducted in search of an observer which gives the possibility of arm tracking. The arms model is based on a two-link manipulator able to move in horizontal and vertical planes. Model is analyzed after linearization and omittance of muscles representing part. The experimental part involves simulation of the motion parameters and real IMU measurements. Finally, simulation results concerning the use of observer in the form of Kalman and particle filters are presented.

The mathematical model of the human arm as a switched linear system

The article presents the process of designing a mathematical model of the human arm. Modelling arm consists of two joints connected by the rotational link. Each of them is represented as a rectangular prism which changes shape during the movement. The moment of shape change depends on the two-state coordinates: the angular displacement q1 and q2. Based on the analysis of the arm movement, a mathematical model has been proposed. The design process was made on the basis of switched systems theory. In the first step, we present the transition from the general equation of the two-link arm dynamics to the state equation for stationary linear models. In the second step, a mathematical model has been shown as a switched linear system. The article also shows that the switching rule depends on the two components of the state vector. A switching method was presented in the schematic drawings.

Dynamics and Optimal Control of Quadrotor Platform

This article is devoted to development of a mathematical model of quadrotor and its applications in the control system of such platform. It shows consecutive steps in developing the equations constituting the model. Various aerodynamic phenomena, such as Vortex Ring State or blade flapping are mentioned and taken into account. The assumptions and reasoning behind are discussed. The structure of a control system is presented. Justification of optimal LQ regulator is made. Simulation tests of control system performance are conducted. Simple way of creating flight trajectories is shown. The conclusions are stated about the level of insight necessary in the creation of a control-oriented and useable model of quadrotor platform.

Model development and optimal control of quadrotor aerial robot

In this article we address the problem of expanding literature-known model of quadrotor dynamics and the benefits it brings. This extended model is used together with LQR controller to show the capability of controlled flight and intuitive 3D trajectory composition.

Developing and Implementation of the Walking Robot Control System

The article presents the walking robot control system project. A ROBONOVA-I robot is used as a base mechanics and servo research platform. The possibilities of this platform allow to control the robot’s limbs with 16 degrees of freedom. Designed control system supports force sensors and three-axis gyroscope with triaxial accelerometer, all in one ADIS16360 system by Analog Device. A PC software is made, which allows to test the pre-developed algorithms. User is able to wirelessly communicate with the robot via XBee module and also to track, online, information from sensors. Article concludes with a simple algorithm for sequentially walking robot.

Mathematical model of the state of acoustic field enclosed within a bounded domain

The article describes a distributed parameter model of the acoustic field for the fluid enclosed within a bounded domain. The model is given in the form of abstract partial differential equations, defined in an appropriate function space. The theory of partial differential equations, as well as certain results from linear functional analysis is used for its formulation and description. The state space representation of the problem is formulated and analyzed by means of above techniques.

Chosen aspects of modeling and control of quadrotor platform

This article is presenting the extended model of quadrotor platform together with a bespoken control system based on optimal approach. It highlights particular aspects of the derived model, such as inclusion of rotor gyroscopic effects and thrust generation based on momentum theory. The controller’s behavior is tested by simulations. Comparisons with literature-available solutions to the problem of full quadrotor optimal control are made and important differences exposed. Conclusions are drawn and future work proposed.

Mathematical Model of a Human Leg

This article presents a novel approach to modelling of the human leg with the use of linear switched systems. Second order differential equations forming a two-segments leg model moving in a vertical plane are shown. State space linear equations describing given model are derived. A linear switched system for such model is presented, where the switching function is modelled as state-dependent. Based on this approach a linear system is presented, which is composed of four subsystems between which switching occurs depending on two state variables. These variables represent angular displacements. As a consequence, a state space division is shown together with a linear system describing human leg in this setting. Finally, a set of simulations presents differences between standard linear modelling approach and a switched linear system approach.

Modelling of the Human's Leg as a Switched Linear System

This article describes the alternative mathematical modelling of a humans leg by means of switched system approach. The leg is considered three joints connected by a rotational link. The novelty of each of the links being represented as a rectangular prism changing shape during motion introduces new possibilities of model application. Each of the links is represented as a rectangular prism whichs shape depends on the three state coordinates - the angular displacements q1, q2 and q3. A design process is then made on the basis of switched system theory. In several steps we show the transition from the general equation of the three-link leg dynamics to the switched linear system where the switching rule depends on the state vector. A switching method is presented in schematics.

Simulation-Based Analysis of a Linear Switched System Based on Human Arm’s Dynamics

The article outlines the process of developing a mathematical model of the human arm. The model arm consists of two joints connected by the rotational link. Each of them is represented as a truncated cone prism which changes its shape during motion. The shape change instant depends on the two-state coordinates being the angular displacements q1 and q2. Based on the analysis of the arm motion a mathematical model is proposed. The design process is made on the basis of switched systems theory. We present a transition from the general equation of a two-link arm’s dynamics to the state equation for stationary linear models. Based on previous step a mathematical model is presented as a switched linear system. The article also shows that the dependency of the switching rule on the two components of the state vector.