MODERN ROBOTICS g
MECHANICS, PLANNING, AND CONTROL
gg gg gg
Practice Exercises
g
ContributionsgfromgTitogFernandez,gKevingLynch,gHuangWeng,gandgZackgWoodr
uff
Decemberg 6,g 2018
Thisg isg ag supplementalg documentg to
ModerngRoboticsgMechanic
s,gPlanning,gandgControlgKevingM.gLy
nchgandgFrankgC.gParkgCambridgegUn
iversitygPress,g2017
Originalgmaterialgfromgthisgdocumentgmaygbegreusedgprovidedgpropergcitation
gisggiven.g Moreginformationgongtheg book,gincludinggag downloadableg preprint,g
software,gvideos,gonlinegcourses,gandgagfeedbackgformgcangbegfoundgatghttp:
//modernrobotics.org.g Commentsgaregwelcome!
,
,Contents
1 Introduction 1
2 Practiceg Exercisesg ong Configurationg Space 3
2.1 Practiceg Exercises ..........................................................................................3
2.2 Solutions.........................................................................................................9
3 Practiceg Exercisesg ong Rigid-Bodyg Motions 15
3.1 Practiceg Exercises ........................................................................................15
3.2 Solutions.......................................................................................................25
4 Practiceg Exercisesg ong Forwardg Kinematics 31
4.1 Practiceg Exercises ........................................................................................31
4.2 Solutions.......................................................................................................36
5 Practiceg Exercisesg ong Velocityg Kinematicsg andg Statics 39
5.1 Practiceg Exercises ........................................................................................39
5.2 Solutions.......................................................................................................43
6 Practiceg Exercisesg ong Inverseg Kinematics 47
6.1 Practiceg Exercises ........................................................................................47
6.2 Solutions.......................................................................................................51
7 Practiceg Exercisesg ong Kinematicsg ofg Closedg Chains 53
7.1 Practiceg Exercises ........................................................................................53
7.2 Solutions.......................................................................................................53
8 Practiceg Exercisesg ong Dynamicsg ofg Openg Chains 55
8.1 Practiceg Exercises ........................................................................................55
8.2 Solutions.......................................................................................................62
Practiceg Exercisesg ong Trajectory Generation 73
9 i
, 9.1 Practiceg Exercises ...................................................................................... 73
9.2 Solutions.......................................................................................................79
10 Practiceg Exercisesg ong Motiong Planning 85
10.1 Practiceg Exercises ........................................................................................85
10.2 Solutions.......................................................................................................85
11 Practiceg Exercisesg ong Robotg Control 87
11.1 Practiceg Exercises ........................................................................................87
11.2 Solutions.......................................................................................................92
12 Practiceg Exercisesg ong Graspingg andg Manipulation 97
12.1 Practiceg Exercises ........................................................................................97
12.2 Solutions.......................................................................................................97
13 Practiceg Exercisesg ong Wheeledg Mobileg Robots 99
13.1 Practiceg Exercises ........................................................................................99
13.2 Solutions..................................................................................................... 101
PracticegexercisesgforgModerngRobotics,gLynchgandgPark,gCambridgegU.gPress,g2017.g http://modernrobotics.or
g
MECHANICS, PLANNING, AND CONTROL
gg gg gg
Practice Exercises
g
ContributionsgfromgTitogFernandez,gKevingLynch,gHuangWeng,gandgZackgWoodr
uff
Decemberg 6,g 2018
Thisg isg ag supplementalg documentg to
ModerngRoboticsgMechanic
s,gPlanning,gandgControlgKevingM.gLy
nchgandgFrankgC.gParkgCambridgegUn
iversitygPress,g2017
Originalgmaterialgfromgthisgdocumentgmaygbegreusedgprovidedgpropergcitation
gisggiven.g Moreginformationgongtheg book,gincludinggag downloadableg preprint,g
software,gvideos,gonlinegcourses,gandgagfeedbackgformgcangbegfoundgatghttp:
//modernrobotics.org.g Commentsgaregwelcome!
,
,Contents
1 Introduction 1
2 Practiceg Exercisesg ong Configurationg Space 3
2.1 Practiceg Exercises ..........................................................................................3
2.2 Solutions.........................................................................................................9
3 Practiceg Exercisesg ong Rigid-Bodyg Motions 15
3.1 Practiceg Exercises ........................................................................................15
3.2 Solutions.......................................................................................................25
4 Practiceg Exercisesg ong Forwardg Kinematics 31
4.1 Practiceg Exercises ........................................................................................31
4.2 Solutions.......................................................................................................36
5 Practiceg Exercisesg ong Velocityg Kinematicsg andg Statics 39
5.1 Practiceg Exercises ........................................................................................39
5.2 Solutions.......................................................................................................43
6 Practiceg Exercisesg ong Inverseg Kinematics 47
6.1 Practiceg Exercises ........................................................................................47
6.2 Solutions.......................................................................................................51
7 Practiceg Exercisesg ong Kinematicsg ofg Closedg Chains 53
7.1 Practiceg Exercises ........................................................................................53
7.2 Solutions.......................................................................................................53
8 Practiceg Exercisesg ong Dynamicsg ofg Openg Chains 55
8.1 Practiceg Exercises ........................................................................................55
8.2 Solutions.......................................................................................................62
Practiceg Exercisesg ong Trajectory Generation 73
9 i
, 9.1 Practiceg Exercises ...................................................................................... 73
9.2 Solutions.......................................................................................................79
10 Practiceg Exercisesg ong Motiong Planning 85
10.1 Practiceg Exercises ........................................................................................85
10.2 Solutions.......................................................................................................85
11 Practiceg Exercisesg ong Robotg Control 87
11.1 Practiceg Exercises ........................................................................................87
11.2 Solutions.......................................................................................................92
12 Practiceg Exercisesg ong Graspingg andg Manipulation 97
12.1 Practiceg Exercises ........................................................................................97
12.2 Solutions.......................................................................................................97
13 Practiceg Exercisesg ong Wheeledg Mobileg Robots 99
13.1 Practiceg Exercises ........................................................................................99
13.2 Solutions..................................................................................................... 101
PracticegexercisesgforgModerngRobotics,gLynchgandgPark,gCambridgegU.gPress,g2017.g http://modernrobotics.or
g
