Design of a Robotic Arm for Laboratory Simulations of Spacecraft Proximity Navigation and Docking

247 Pages·2013·7.22 MB·English

Università degli Studi di Padova
Dipartimento di Ingegneria Industriale

Corso di Laurea Magistrale in Ingegneria Aerospaziale

Tesi di Laurea Magistrale in Ingegneria
Aerospaziale

Design of a Robotic Arm for Laboratory
Simulations of Spacecraft Proximity
Navigation and Docking

Relatore: Prof. Alessandro Francesconi

Laureando: Andrea Antonello

ANNO ACCADEMICO 2012-2013

To my families, in Italy and California.
To you, Silvia.

Contents
1 Introduction 1
1.1 A long journey . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation and state of the art . . . . . . . . . . . . . . . . . 3
1.3 Robot preliminary design . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.2 Mechanical structure . . . . . . . . . . . . . . . . . . . 12
1.3.3 End-effector configuration . . . . . . . . . . . . . . . . 17
1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2 Kinematics 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Denavit-Hartenberg convention . . . . . . . . . . . . . . . . . 22
2.3 Direct Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Inverse Kinematics . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.1 Pieper’s solution . . . . . . . . . . . . . . . . . . . . . 28
2.4.2 Alternate algebraic solution . . . . . . . . . . . . . . . 32
2.4.3 Methods comparison . . . . . . . . . . . . . . . . . . . 34
2.5 Differential kinematics . . . . . . . . . . . . . . . . . . . . . . 35
2.5.1 Geometric approach . . . . . . . . . . . . . . . . . . . 36
2.5.2 Inverse differential kinematics . . . . . . . . . . . . . . 39
2.5.3 Singularities . . . . . . . . . . . . . . . . . . . . . . . . 41
2.6 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.6.1 Rectilinear trajectory . . . . . . . . . . . . . . . . . . . 44
2.6.2 Circular trajectory . . . . . . . . . . . . . . . . . . . . 47
2.7 Model verification: Simulink’s SimMechanics toolbox. . . . . . 51
3 Trajectory definition 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Main approaches . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3 Joint space planning . . . . . . . . . . . . . . . . . . . . . . . 58
3.3.1 Point-to-point motion with intermediate via points . . 61
3.4 Operational space planning . . . . . . . . . . . . . . . . . . . 62
3.4.1 Predefined analytical path . . . . . . . . . . . . . . . . 63
3.4.2 Corrected on the go . . . . . . . . . . . . . . . . . . . . 69
4 Dynamics 71
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Euler-Lagrange method . . . . . . . . . . . . . . . . . . . . . . 71
4.3 Euler-Newton method . . . . . . . . . . . . . . . . . . . . . . 73
4.3.1 The Euler-Newton routine . . . . . . . . . . . . . . . . 73
4.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.4.1 Rectilinear trajectory . . . . . . . . . . . . . . . . . . . 78
4.4.2 Circular trajectory . . . . . . . . . . . . . . . . . . . . 83
4.5 Model verification: Simulink’s SimMechanics toolbox. . . . . . 87
5 Linear Feedback Control 93
5.1 Joint space control . . . . . . . . . . . . . . . . . . . . . . . . 93
5.1.1 Decentralized control . . . . . . . . . . . . . . . . . . . 94
5.1.2 Design of the PD compensator . . . . . . . . . . . . . . 99
5.1.3 Design of the PID compensator . . . . . . . . . . . . . 105
5.1.4 Extension to a multibody system . . . . . . . . . . . . 109
5.2 Operational space control . . . . . . . . . . . . . . . . . . . . 110
5.2.1 An overview . . . . . . . . . . . . . . . . . . . . . . . . 111
6 Space trajectory analyis 115
6.1 Orbital mechanics review . . . . . . . . . . . . . . . . . . . . . 116
6.1.1 Relative motion in orbit . . . . . . . . . . . . . . . . . 116
6.2 CW equations: main applications . . . . . . . . . . . . . . . . 121
6.2.1 Relative free motion simulation . . . . . . . . . . . . . 121
6.2.2 Relative motion with quasi-constant disturbances . . . 122
6.2.3 Relative motion with impulsive disturbances . . . . . . 123
6.2.4 Relative motion with ADCS control . . . . . . . . . . . 126
6.3 Force sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Matlab simulation . . . . . . . . . . . . . . . . . . . . . . . . . 131
6.4.1 Rendezvous maneuver . . . . . . . . . . . . . . . . . . 131
6.4.2 Rendez-vous maneuver with impulsive disturbance . . . 134
6.4.3 Rendezvous approach with on the go corrections . . . . 138
7 Sizing 143
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.2 Link design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.2.1 Material choice . . . . . . . . . . . . . . . . . . . . . . 145
7.2.2 Load analysis . . . . . . . . . . . . . . . . . . . . . . . 146
7.2.3 Buckling analysis . . . . . . . . . . . . . . . . . . . . . 155
7.3 Motor choice . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.3.1 Motor types . . . . . . . . . . . . . . . . . . . . . . . . 162
7.3.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . 164
7.3.3 Hardware selection . . . . . . . . . . . . . . . . . . . . 170
7.4 Final data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
7.5 SolidWorks renders . . . . . . . . . . . . . . . . . . . . . . . . 174
CAD Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Assembly 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Assembly 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Assembly 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Assembly 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
Assembly 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
8 Conclusions and future work 191
Appendices 205
A Matlab Scripts 207
Matlab Scripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
B Jacobian expression 229
C Datasheets 231
EC 90 datsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
EC 45 datsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
ATI Nano 17 datsheet . . . . . . . . . . . . . . . . . . . . . . . . . 236
Abstract
The increasing number of human objects in space has laid the foundation of a novel class
of orbital missions for servicing and maintenance. The main goal of this thesis is the de-
velopment of a robot manipulator for the simulation of close approach orbital maneuvers,
with particular attention to docking and capture. There are currently very few facilities
able to simulate relative motion between orbiting objects: DLR’s EPOS experiment is
the leading edge of European research on RvD ground simulations. The 25m long test-
ing site consists in two industrial anthropomorphic robots that can reproduce docking
and berthing scenarios, taking into account dynamic contacts, gravity and even sunlight
illumination for utmost realistic simulations. This project tries to propose a viable alter-
native to these huge and costly RvD structures; the addition of force sensing transducers
and the possibility to dynamically scale the simulations makes the manipulator a cheap
and portable hardware-in-the-loop testing bench for orbital phenomena. After selecting
the most dexterous robotic configuration, the kinematic and dynamic problems were ana-
lyzed; a basic PID controller was then implemented and its stability to step response and
disturbances successfully verified. An extended simulation campaign, comprising Matlab
and SimMechanics environments, confirmed the theoretical models and allowed to repro-
duce typical rendezvous and docking maneuvers (providing useful data for the sizing). By
integrating a force sensor, it was possible to impose and simulate orbital motion and to
account for any force disturbance. With information deriving on structural analyses and
dynamics extrapolations, a preliminary design was carried out, and led to the translation
ofthetheoreticalrequirementsintothesizingandselectionofthestructure, thehardware
and the actuators. The final robot is able to simulate RvDs inside a spherical working
space of 1.3m radius, with a total mass of just 7.5kg. This thesis sets the foundations
for the physical realization of the arm, which will serve as an innovative platform for a
multidisciplinary satellite testing facility.