Prototyping Dynamic Robots

Prototyping Dynamic Robots: Lessons from the UCSD Coordinated Robotics Lab

Nick Morozovsky, PhDRobotics Consultant

March 17, 2015

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UCSD CoordinatedRobotics Lab

Nick Morozovsky Mar 17, 2015

Outline

• Introduction

• Tools

• Switchblade

• SkySweeper

• Conclusions

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Outline

• Introduction

• Tools

• Switchblade

• SkySweeper

• Conclusions

3



Introduction

• Hardware revolution is underway

• Robotics is a subset, what is a robot anyway?

• Barriers to entry in developing hardware are plummeting

• Driven by low-cost, capable components, software tools, and global communications

• The line between hardware and software is being blurred.

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http://makezine.com/projects/make-43/smart-rat-trap/

http://makezine.com/projects/make-43/smart-rat-trap/



Introduction

• Proliferation of low-cost and capable microprocessors and sensors

• 3D Robotics CEO Chris Anderson’s “peace dividend of the smartphone war”

• Accelerometers, gyroscopes, magnetometers, light sensors, cameras, GPS, WiFi, Bluetooth, etc.

• Additive manufacturing (3D printing) has dropped two orders of magnitude in price

• Rapid prototyping on your desk

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Introduction

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from Cyril Ebersweiler’s Hardware trends 2015 slidesharehttp://www.slideshare.net/haxlr8r/hardware-trends-2015or search: slideshare hardware trends

http://www.slideshare.net/haxlr8r/hardware-trends-2015



Introduction Robotics Challenges

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MobilityPerception

Manipulation“Go get me a beer from the

fridge”

Stairs

Openinga door

SandEggs

Unstructuredterrain

Where tograsp object

LocalizationMapping



Outline

• Introduction

• Tools

• Switchblade

• SkySweeper

• Conclusions

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Tools Mechanical Engineering

• 3D printing

• Multiple materials are here, and more are coming

• New generation of CAD tools

• TinkerCAD

• OpenSCAD

• Onshape

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Tools Electrical Engineering

• Eagle CAD

• SparkFun library

• Fritzing

• Unique breadboard view

• CircuitMaker

• powered by Altium

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Tools Electrical Engineering

• Voxel8 Multi-material 3D printer

• Autodesk Project Wire

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Tools Software Engineering

• Explosion of single board computers

• Arduino, Raspberry Pi, BeagleBone, Spark, etc. communities

• Almost any sensor or actuator you’re trying to interface has already been interfaced

• Pay attention to licenses and be a good community member

• ROS: Robot Operating System

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Tools Funding

• Bootstrapping

• Accelerators/Incubators

• Increasing number of hardware accelerators

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Tools Crowdfunding

• Just posting on Kickstarter does not guarantee success!

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Tools Crowdfunding

15

from Cyril Ebersweiler’s Hardware trends 2015 slidesharehttp://www.slideshare.net/haxlr8r/hardware-trends-2015or search: slideshare hardware trends

http://www.slideshare.net/haxlr8r/hardware-trends-2015



Tools Complementary Filter

• MEMS accelerometer can measure absolute angle of gravity vector

• Susceptible to high frequency noise and body accelerations

• MEMS gyroscope can be integrated to measure incremental angle

• Susceptible to thermal drift and integration error

• Use complementary filter to combine accelerometer and gyroscope measurements

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atan2

1/s

Low Pass

High Pass

s

Accelerometer

Gyroscope

Encoder

++

++

++ �

✓

✓

�

µGHP =1/!c

1/!c + h, µALP =

h

1/!c + h



Tools Encoder Velocity Estimation

• Limited by encoder and clock resolution

• Quadrature sub-periods are not equal

• Measure four separate periods

• Average multiple periods when possible (M ≥ 2)

• Bound low speed by time since last edge (M < 1)

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A

ARF

B

AFR

BFR BRF

AR BR BR AF AF BF BF AR

ARR

BFF

M =2!hCPR

⇡



Tools Lagrangian Dynamics

• Powerful dynamics formulation

• Apply constraints with Lagrange multiplier

• Broadly applicable to a large class of robotic systems

• Can be applied programmatically

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L = T � V

d

dt

✓�L�qi

◆� �L

�qi= Qi

M(q)q + F (q, q) = Q

A(q)q = 0

M(q)q + F (q, q) = Q+A(q)T�

S(q) = null[A(q)]

S(q)TM(q)q + S(q)TF (q, q) = S(q)TQ



Tools Lagrangian Dynamics

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q = S⌫, q = S⌫, S

TM(q)S⌫ + S

TF (q, q) = S

TQ

⌫ = [STM(q)S]�1

S

T [Q� F (q, q)]

q = S[STM(q)S]�1

S

T [Q� F (q, q)]

Q = B⌧ = B[⌃u� Z(q)]

qr =¯S⌫, qr =

¯S⌫, x =

✓qr

qr

◆, x = f(x) + �(x)u

f(x) =

✓qr

�¯S[ST

M(q)S]�1S

T [BZ(q) + F (q, q)]

◆

�(x) =

✓0n⇥nu

¯S[ST

M(q)S]�1S

TB⌃

◆



Tools Equilibrium Manifold

• Solve for (unstable) equilibrium manifold from dynamics by setting accelerations and velocities to zero

• Equivalent to static analysis, setting Newton’s 2nd Law equal to zero and setting center of mass over contact point

• u* is a feedforward term when the equilibrium requires non-zero control input

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⌫ = [STM(q)S]�1

S

T {B[⌃u� Z(q)]� F (q, q)} = 0nr⇥1

S

T {B[⌃u⇤ � Z(0n⇥1)]� F (q⇤, 0n⇥1)} = 0nr⇥1

x = x� x

⇤, u = u� u

⇤

˙x = f(x+ x

⇤) + �(x+ x

⇤)(u+ u

⇤)



Tools Linearization & Integral Control

• Linearize about reference position

• Integrate regulation error

• Discretize with sample time h

• State feedback matrix from LQR

• Can be applied programmatically

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˙x =Ax+ B(u+ u

⇤)

A =�f(x+ x

⇤)

�x

��x=0

, B = �(x+ x

⇤)��x=0

⇠ =Cx, x =

✓x

⇠

◆,

˙x = Ax+ B(u+ u

⇤)

A =

A 02n⇥nu

C 0ni⇥nu

�, B =

B

0ni⇥nu

�

x

k+1 =Fx

k

+G(uk

+ u

⇤)

F =eAh

, G =

Zh

0eA⌘Bd⌘

u =K

✓x� x

⇤

⇠

◆+ u

⇤



Outline

• Introduction

• Tools

• Switchblade

• SkySweeper

• Conclusions

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Switchblade

• Tread assemblies can pivot w.r.t. the central chassis

• Significantly changes the center of mass

• Different modes of locomotion

• Applications: search & rescue, border patrol, mine exploration, toy/entertainment, general research platform

• Patent pending

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Switchblade Perching Dynamics

• Constraint matrices combine no-slip condition and different stiction states

• Power function accounts for rate of energy dissipation due to coulomb friction

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θ

αϕ

LT

LC

rmT

mC

w

mS

XYρ

w =� r(�� ↵)� ⇢(⇡/2� ↵)

P =� µkmgr

sin↵(�� ↵)� cT (↵� ✓)

�P

�q=

0

BB@

0�µkmgr

sin↵ · sgn(�� ↵)µkmgrsin↵ · sgn(�� ↵)� cT · sgn(↵� ✓)

cT · sgn(↵� ✓)

1

CCA , q =

0

BB@

w�↵✓

1

CCA



Switchblade Mechanical Design

• Two degree of freedom hip joint

• Two independent torques transmitted coaxially

• Continuous rotation

• Motors, sensors, and battery in chassis–simplifies wiring

• Leverage symmetry to reduce unique part count

• Sheets of plastic laser cut into parts

• Tabs and slots speed up assembly and reduce the number of fasteners needed

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Switchblade

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Switchblade Perching

• Friction compensator improves performance

• Oscillation is due to stiction

• Performance limited by mass distribution and friction

270 1 2 3 4 5 6 7 8 9 10

−0.5

0

0.5

1

1.5

2

T ime (se c )

Angle

(rad)

φ

α

θφ∗

α ∗

θ ∗

0 1 2 3 4 5 6 7 8 9 10

−1.92

−1.9

−1.88

−1.86

−1.84

−1.82

−1.8

−1.78

−1.76

T ime (se c )

φ−

α(rad)

0 1 2 3 4 5 6 7 8 9 10

−1

−0.5

0

0.5

1

T ime (se c )

φ−

α(rad/se

c)

Ex p e rimental a S = 0

Exp e rimental a S = 0 .06

S imu lation a S = 0

S imu lation a S = 0 .06

φ∗− α ∗

θ

αϕ

LT

LC

rmT

mC

w

mS

XYρ



Outline

• Introduction

• Tools

• Switchblade

• SkySweeper

• Conclusions

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SkySweeper

• 2 identical links pivotally connected by rotary series elastic actuator (SEA) hub

• 3 position actuated clamp

(a) Open

(b) Rolling - allows axial translation

(c) Pivoting

• Presented at IROS 2013 in Tokyo

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SkySweeper Inchworm

• One pivoting clamp and one rolling clamp

• SEA actuates to increase the angle between the links

• Switch clamp configuration, decrease the angle between the links, repeat

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SkySweeper Swing-Up

• One pivoting clamp and one open clamp

• Sine sweep control input to the SEA

• Second clamp closes once it reaches cable

• Useful for installation on the cable

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SkySweeper Backflip

• One pivoting clamp and one open clamp

• Preload SEA, release one clamp, swing to grab other end, repeat

• Circumvent obstacle on the cable

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!

"

�

xy

JL ,mL

JL ,mL

JJ

2L

2L

1

2

SkySweeper Dynamics

• Dynamic constraints depend on the configuration of the clamps

• 0, 1, or 2 constraints per clamp

• Holonomic vertical constraint when clamp is rolling or pivoting

• Additional non-holonomic horizontal constraint when clamp is pivoting

• Stack applicable constraint matrices and find orthonormal basis for null space

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y = 0

Ay1(q) = (0 1 0 0 0)

x = 0

A

x1(q) = (1 0 0 0 0)

y � 2L(cos ✓ + cos↵) = 0

Ay2(q) = (0 1 2L sin ✓ 0 2L sin↵)

x+ 2L(

˙

✓ cos ✓ + ↵ cos↵) = 0

A

x2(q) = (1 0 2L cos ✓ 0 2L cos↵)

q =�x y ✓ � ↵

�T



SkySweeper Finite State Machine Controller

• Actions: clamp positions, SEA

• Transitions defined by sensor readings: spring deflection, separation angle, cable detection

• Implemented in code as a switch structure

• Simulation performed with switched system of equations of motion with different constraint matrices

!+π-# > 1.9

!+π-# < 1.0

State 0: OpenClamp 1: PivotingClamp 2: Rollingu = -0.65

State 1: CloseClamp 1: RollingClamp 2: Pivotingu = 0.40

State 8: Swing 1Clamp 1: PivotingClamp 2: Openu = -0.20

State 9: Charge 2Clamp 1: PivotingClamp 2: Pivotingu = 1

Cable in grasp of clamp 2

State 7: Charge 1Clamp 1: PivotingClamp 2: Pivotingu = -1

!-γ > 1

State 10: Swing 2Clamp 1: OpenClamp 2: Pivotingu = 0.20

!-γ < -1


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State 5: SwingClamp 1: PivotingClamp 2: Openu = 0.7t*sin(π t)

State 6: HoldClamp 1: PivotingClamp 2: Pivotingu = 0


Inchworm

Swing-Up

Backflip



SkySweeper Design

• 3D printed parts with off the shelf electronics

• 3 position actuated clamp

• Servo drives symmetrically coupled clamp arms

• Magnets align clamps, teeth prevent rotation in pivoting position

• IR emitter and phototransistor pair detect cable

• Series elastic actuator (SEA) hub

• DC motor and two unidirectional torsion springs

• Energy storage for dynamic maneuvers

• Potentiometers measure spring deflection and angle between links

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SkySweeper Inchworm

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SkySweeper Inchworm

• Simulation matches experimental results, although greater spring deflection is predicted

• 50ms delay in switching clamp positions

• Unmodeled effects of slippage and rope vibration contribute to the discrepancy between plots

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0 0.5 1 1.5 2 2.5 3 3.50.5

1

1.5

2

2.5

t(s)

Link

Sep

arat

ion

θ + π − α

(rad

)

0 0.5 1 1.5 2 2.5 3 3.5−0.5

0

0.5

1

1.5

t(s)

Sprin

g D

efle

ctio

nα

− γ

(rad)

SimulationExperimental



SkySweeper Swing-Up

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SkySweeper Backflip

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Outline

• Introduction

• Tools

• Switchblade

• SkySweeper

• Conclusions

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Conclusions Nick’s Rules of Robotics

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1. Never disassemble a working robot.

1. Always have a demo ready.

2. Video or it didn’t happen.

2. If it works the first time, you’re testing it wrong.

1. How good is good enough? Have defined metrics.

2. If you can’t measure it, you can’t control it.

3. When in doubt, lubricate.




4. Never underestimate the estimation problem.

1. “but it works in simulation”

5. If specs for a part are listed differently in two places, they’re both wrong.

1. How can you validate it yourself? Or deal with uncertainty?

6. Glue, tape, and zip-ties are not engineering solutions (though they might work in a pinch).

1. You should be able to open your robot.

2. The component that’s hardest to access will be the first to fail.

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7. Do not leave lithium polymer batteries charging unattended.

1. It’s not worth the risk.

2. Use a charging sack.

8. Always have a complete CAD model, including screws and fasteners, before constructing your robot.

1. Plan out order of operations for assembly.

2. Have extra parts on hand.

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9. Avoid using slip rings if at all possible.

1. Intermittent contact, high/variable resistance

10.Clamping collars are always better than set screws.

1. If you have to use set screws (e.g. for cost reasons), use a driving flat and an appropriate thread-locking agent.

11.Always check polarity before plugging a component into a power source.

1. Label battery connectors and components.

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ServoCity.com clamping hub

http://ServoCity.com



Conclusions Acknowledgments

• Advisor: Professor Thomas Bewley

• Chris Schmidt-Wetekam, Andrew Cavender

• Members of the Coordinated Robotics Lab at UCSD

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Technology

Prototyping Dynamic Robots