Karol Seweryn

Optimization of the Trajectory of a General Free - Flying Manipulator During the Rendezvous Maneuver

The paper is focused on the dynamics of a manipulator mounted on a free-flying satellite performing rendezvous and docking maneuver (RVD). The target satellite is assumed to be passive, without attitude control and telecommunication link. The servicing satellite performs, by means of thrusters, a fly - by maneuver, in which it approaches the target satellite on a non-collision path. In the last phase of the RVD maneuver, when the 6dof manipulator executes a predefined path towards the target, it can disturb the dynamics and, in consequence, the trajectory of the servicing satellite. The system (satellite + manipulator) is nonholonomic and its linear momentum and angular momentum are not conserved. The paper describes the algorithm of the manipulator trajectory planning, based on the calculus of variation, which can solve (n+6) dof problem. The cost functional trades off power use of the DC motor and additional conditions constraining the end-effector motion so that it reaches the final desired state expressed as the linear and angular position and velocity. The behavior of the system is described in the Lagrangian formulation and the collocation method is chosen to solve the boundary value problem. The initial trajectory is calculated using the Generalized Jacobian Matrix (GJM) approach that is extended to the system, in which linear and angular momentum is not conserved. An example is provided that shows the optimal trajectory of the LBR manipulator during the RVD maneuver to a tumbling satellite.

Control System for Free-Floating Space Manipulator Based on Nonlinear Model Predictive Control (NMPC)

Manipulator mounted on an unmanned satellite could be used for performing orbital capture maneuver in order to repair satellites or remove space debris from orbit. Use of manipulators for such purposes presents unique challenges, as high level of autonomy is required and the motion of the manipulator influences the position and orientation of the manipulator-equipped satellite. This paper presents a new control system that consists of two modules: trajectory planning module (based on trajectory optimization algorithm) and Model Predictive Controller. Both modules take into account the free-floating nature of the satellite-manipulator system. Proposed control system was tested in numerical simulations performed for a simplified planar case. In the first set of simulations Nonlinear Model Predictive Control (NMPC) was used to ensure realization of a square reference end-effector trajectory, while in the second set control system was used for optimizing and then ensuring realization of the trajectory that leads to grasping of the rotating target satellite. Simulations were performed with disturbances and with the assumed non-perfect knowledge of parameters of the satellite-manipulator system. Results obtained with NMPC are better than results obtained with the controller based on the Dynamic Jacobian inverse and with the Modified Simple Adaptive Control (MSAC).

Trajectory Planning and Simulations of the Manipulator Mounted on a Free-Floating Satellite

This chapter focuses on the dynamics of a 6 DOF manipulator mounted on a satellite during an orbital servicing mission. Algorithm for computation of control torques applied in manipulator’s joints in various parts of orbital rendezvous maneuver is presented. This algorithm can be used to calculate manipulator’s control torques along with torques and forces for control of satellite’s orientation and position during complex maneuver or for controlling only the manipulator while taking into account additional 6 DOFs of the free-floating satellite. Simulation tool used for performing numerical simulations of orbital rendezvous and results of simulations of two parts of the possible maneuver (capturing of tumbling target satellite and positioning captured satellite for docking) are also presented.

Dynamic Simulations of Free-Floating Space Robots

This paper focuses on the dynamics of a 6-dof manipulator mounted on a free-flying servicer satellite during final part of an on-orbit rendezvous maneuver. Determination of reaction torques induced by the manipulator on the servicer satellite is critical for the development of the Guidance, Navigation and Control (GNC) subsystem. Presented in this paper is a path planning algorithm for capturing a tumbling target satellite, as well as simulation results of the capture maneuver and folding of the manipulator with the attached target satellite. The second part of this paper is focused on the presentation of our work leading to the construction of a planar air-bering test-bed for space manipulators.

Analytical Model of Eddy Currents in a Reaction Sphere Actuator

A recently proposed technique to control the satellite attitude using a magnetically levitated sphere requires the development of suitable models of its dynamics. One of the phenomena that can affect motion of the system are eddy currents induced in the stator of the actuator due to time variable magnetic field generated by rotational motion of a permanent magnet rotor. We present an analytical model of the eddy currents for the actuator with eight-pole rotor. The model is derived using a second-order vector potential-based approach, and the solution is obtained in terms of spherical harmonic functions. This model allows us to study rotor rotations with constant angular frequency around an axis arbitrarily oriented with respect to both rotor and stator of the reaction sphere actuator.

Experimental demonstration of singularity avoidance with trajectories based on the Bézier curves for free-floating manipulator

Path planning problem for a free-floating space manipulator can be solved in Cartesian space. In such approach, inverse kinematics is solved on the velocity level using the manipulator Jacobian, but dealing with dynamic singularities may be problematic. In this study, we present application of the Bézier curves for path planning. Modifications of curve shape allow avoidance of singularities. The selection of the Bézier curve parameters responsible for its shape is intuitive and simple. The demonstration of the proposed method was performed for a real system using planar air-bearing microgravity simulator. Experimental results are in agreement with the results of the numerical simulations.

Controlled zero dynamics feedback linearization with application to free-floating redundant orbital manipulator

The paper presents a method of controlling the zero dynamics in nonlinear MIMO feedback linearized system. The method is based on the input signal projection on the decoupling matrix kernel, which leaves the linearized output invariant while controlling the zero dynamics part of the system. The application of the method to the control of space manipulator is proposed.

The Dynamics Influence of the Attached Manipulator on Unmanned Aerial Vehicle

The chapter describes the development and operation of Unmanned Aerial Vehicle (UAV) type flying robot with attached manipulator. The hardware, software architecture and mathematical description of the system used to control the robot is presented. The results of test rigs connected with flying the robot with attached manipulator have been presented and discussed.

Instrument data processing unit for spectrometer/telescope for imaging x-rays (STIX)

The Spectrometer/Telescope for Imaging X-rays (STIX) is one of 10 instruments on board Solar Orbiter, an M-class mission of the European Space Agency (ESA) scheduled to be launch in 2017. STIX applies a Fourier-imaging technique using a set of tungsten grids in front of 32 pixelized CdTe detectors to provide imaging spectroscopy of solar thermal and non-thermal hard X-ray emissions from 4 to 150 keV. These detectors are source of data collected and analyzed in real-time by Instrument Data Processing Unit (IDPU). Besides the data processing the IDPU controls and manages other STIX’s subsystems: ASICs and ADCs associated with detectors, Aspect System, Attenuator, PSU and HK. The instrument reviewed in this paper is based on the design that passed the Instrument Preliminary Design Review (IPDR) in early 2012 and Software Preliminary Design Review (SW PDR) in middle of 2012. Particular emphasis is given to the IDPU and low level software called Basic SW (BSW).

Application of Rapidly-exploring Random Trees (RRT) algorithm for trajectory planning of free-floating space manipulator

Unmanned manipulator-equipped satellite could perform on-orbit servicing mission or could be used to remove large space debris from orbit. Planning a manipulator trajectory that will lead to a safe capture of a selected grasping point on the target object is a challenging task, as the satellite-manipulator system is in a free-floating state. Moreover, complicated structure of the target satellite (e.g., arrays of solar panels) results in obstacles that must be avoided by the satellite-manipulator system. In this paper we present application of Rapidly-exploring Random Trees (RRT) algorithm for trajectory planning of such system. This algorithm proved to be well suited for a considered case, as state of the satellite-manipulator system is highly dimensional (12 + 2n dimensions) and various constraints must be taken into account (e.g., joint limits and obstacles). Operation of the RRT algorithm is successfully demonstrated in a simplified simulation example.