Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
ECE 486 Lecture
Search
Safwan Choudhury
June 06, 2012
Education
0
320
ECE 486 Lecture
Safwan Choudhury
June 06, 2012
Tweet
Share
More Decks by Safwan Choudhury
See All by Safwan Choudhury
Design and Gait Synthesis for a 3D Lower Body Humanoid
safwanc
1
73
Controlling Wheelchair Motion with Electroencephalography
safwanc
3
180
Accurate Determination of Joint Angles from Inertial Measurement Unit Data
safwanc
0
180
Gait Controller for 3D Active Dynamic Walking
safwanc
0
150
Bipedal Locomotion
safwanc
2
67
Learning Thought-Based Motor Control using Gaussian Processes
safwanc
0
130
Analysis of the Foot Placement Estimator
safwanc
0
200
Electromechanical Design
safwanc
0
150
Other Decks in Education
See All in Education
登壇未経験者のための登壇戦略~LTは設計が9割!!!~
masakiokuda
3
550
SkimaTalk Teacher Guidelines
skimatalk
0
790k
Tangible, Embedded and Embodied Interaction - Lecture 7 - Next Generation User Interfaces (4018166FNR)
signer
PRO
0
1.7k
ふりかえり研修2025
pokotyamu
0
1.2k
新卒交流ワークショップ
pokotyamu
0
440
(キラキラ)人事教育担当のつらみ~教育担当として知っておくポイント~
masakiokuda
0
110
より良い学振申請書(DC)を作ろう 2025
luiyoshida
1
3.3k
OpenSourceSummitJapanを運営してみた話
kujiraitakahiro
0
720
2025年度春学期 統計学 第3回 クロス集計と感度・特異度,データの可視化 (2025. 4. 24)
akiraasano
PRO
0
130
AIC 103 - Applications of Property Valuation: Essential Slides
rmccaic
0
230
Tutorial: Foundations of Blind Source Separation and Its Advances in Spatial Self-Supervised Learning
yoshipon
1
120
Course Review - Lecture 12 - Next Generation User Interfaces (4018166FNR)
signer
PRO
0
1.7k
Featured
See All Featured
Making the Leap to Tech Lead
cromwellryan
134
9.4k
Why You Should Never Use an ORM
jnunemaker
PRO
58
9.4k
Scaling GitHub
holman
460
140k
Imperfection Machines: The Place of Print at Facebook
scottboms
267
13k
GitHub's CSS Performance
jonrohan
1031
460k
Let's Do A Bunch of Simple Stuff to Make Websites Faster
chriscoyier
507
140k
Done Done
chrislema
184
16k
StorybookのUI Testing Handbookを読んだ
zakiyama
30
5.9k
Intergalactic Javascript Robots from Outer Space
tanoku
271
27k
A Tale of Four Properties
chriscoyier
160
23k
Reflections from 52 weeks, 52 projects
jeffersonlam
351
20k
Building a Scalable Design System with Sketch
lauravandoore
462
33k
Transcript
ECE 486: Robot Dynamics and Control Practical Applications of the
Jacobian Safwan Choudhury May 31, 2012
Brief Introduction
Bipedal Locomotion
Bipedal Robot 14 DOF Lower Body
q3 q2 q1
q4 q5
q7 q6
Electromechanical Design SolidWorks + Custom Toolchain
High Performance Direct Drive Micromo DC Motors + Misumi Drivetrain
Components
Machined on Campus Engineering Machine Shop (E3)
Full Dynamic Simulations Simulink + SimMechanics + QUARC
Basic Joint Control 7DOF Leg w/ Fixed Base
The Jacobian Differential Kinematics ˙ x = J ˙ q
Computing the Jacobian Columns The “Geometric” Approach Recall
Computing the Jacobian Columns The “Geometric” Approach Revolute Joints Ji
= zi 1 ⇥ ( on oi 1) zi 1 Ji = zi 1 0 Prismatic Joints Recall
Why?
Motivating Example q dq QUARC Visualization System Timebase Kp KP(1:7)
Knee Pitch 60 Kd KD(1:7)*5 Hip Yaw 0 Hip Roll 0 Hip Pitch -30 EN 1 D2R D2R D2R D2R D2R D2R D2R Biped τ q q′ q′′ Ankle Yaw 0 Ankle Roll 0 Ankle Pitch -20 Direct Joint Control
Motivating Example Direct Joint Control
What about complex motions? Inverse Kinematics? Other Methods?
Jacobian Inverse Control Differential Kinematics ˙ q = J 1
˙ x
Jacobian Inverse Control 1. Compute Jacobian matrix w.r.t. end effector
2. Invert the matrix (pseudoinverse if ) 3. Obtain by multiplying 4. Obtain by integrating ˙ q q = Z ˙ q q ˙ q = J 1 ˙ x n > 6
Motivating Example Work Space Analysis QUARC Visualization Trajectory Reference Model
Configuration Joint Space Analysis Jacobian Inverse Transformation q′ = J-1x′ J x′ q q′ Jacobian Computation DQREF QREF q → x q x x dqref qref Jacobian Inverse Control
Motivating Example τ q q′ q′′ PD Controller q error
q′ error τ control erse Transformation q′ = J-1x′ q q′ an Computation Control Torques DQREF QREF q → x q q dq dqref qref Jacobian Inverse Control
Motivating Example Jacobian Inverse Control
Motivating Example Jacobian Inverse Control
Jacobian Transpose Control Differential Kinematics ⌧ = JT F
Gravity Compensation Center of Mass (COM) as an End Effector
Motivating Example Without Gravity Compensation
Computing the Jacobian Columns The “Geometric” Approach Recall
Center of Mass Equation Rigid Body Physics Recall xcom =
P ximi P mi
Gravity Compensation Center of Mass (COM) as an End Effector
Partial Center of Mass Rigid Body Physics
Jacobian Transpose Control 1. Compute the partial center of masses
for each joint 2. Form the COM Jacobian matrix 3. Obtain from the basic formula 4. Obtain by multiplying J com ~ FG = m~ g ~ F ⌧G ⌧ G = JT com ~ F G
Jacobian Transpose Control With Gravity Compensation
Whole Body Control A Jacobian-Based Approach ˙ q = 2
6 6 4 JCOM J1 J2 J3 3 7 7 5 1 ˙ x
Independent Leg Motions Two Jacobian’s Stacked: JL + JR
Shifting Balance Three Jacobian’s Stacked: JCOM + JL + JR
Questions?