Prototyping Dynamic Robots
3 likes651 views
The document presents insights from the UCSD Coordinated Robotics Lab regarding the development of dynamic robots, emphasizing the hardware revolution and the diminishing barriers for hardware creation. It discusses various tools and technologies, including 3D printing, software frameworks, and funding strategies essential for robotics development. Additionally, two specific robotic platforms, Switchblade and Skysweeper, are highlighted for their innovative designs and applications in fields like search and rescue and research.
![UCSD Coordinated
Robotics Lab
Nick Morozovsky Mar 17, 2015
Tools
Lagrangian Dynamics
• Powerful dynamics
formulation
• Apply constraints with
Lagrange multiplier
• Broadly applicable to a
large class of robotic
systems
• Can be applied
programmatically
18
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)T
M(q)¨q + S(q)T
F(q, ˙q) = S(q)T
Q](https://image.slidesharecdn.com/roboticsclubtalk-150318003537-conversion-gate01/85/Prototyping-Dynamic-Robots-18-320.jpg)
![UCSD Coordinated
Robotics Lab
Nick Morozovsky Mar 17, 2015
Tools
Lagrangian Dynamics
19
˙q = S⌫, ¨q = S ˙⌫, ST
M(q)S ˙⌫ + ST
F(q, ˙q) = ST
Q
˙⌫ = [ST
M(q)S] 1
ST
[Q F(q, ˙q)]
¨q = S[ST
M(q)S] 1
ST
[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] 1
ST
[BZ( ˙q) + F(q, ˙q)]
◆
(x) =
✓
0n⇥nu
¯
S[ST
M(q)S] 1
ST
B⌃
◆](https://image.slidesharecdn.com/roboticsclubtalk-150318003537-conversion-gate01/85/Prototyping-Dynamic-Robots-19-320.jpg)
![UCSD Coordinated
Robotics Lab
Nick Morozovsky Mar 17, 2015
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
20
˙⌫ = [ST
M(q)S] 1
ST
{B[⌃u Z( ˙q)] F(q, ˙q)} = 0nr⇥1
ST
{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⇤
)](https://image.slidesharecdn.com/roboticsclubtalk-150318003537-conversion-gate01/85/Prototyping-Dynamic-Robots-20-320.jpg)
Prototyping Dynamic Robots
- 1. Prototyping Dynamic Robots: Lessons from the UCSD Coordinated Robotics Lab Nick Morozovsky, PhD Robotics Consultant March 17, 2015 1
- 2. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Outline • Introduction • Tools • Switchblade • SkySweeper • Conclusions 2
- 3. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Outline • Introduction • Tools • Switchblade • SkySweeper • Conclusions 3
- 4. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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. 4 http://makezine.com/projects/make-43/smart-rat-trap/
- 5. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 5
- 6. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Introduction 6 from Cyril Ebersweiler’s Hardware trends 2015 slideshare http://www.slideshare.net/haxlr8r/hardware-trends-2015 or search: slideshare hardware trends
- 7. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Introduction Robotics Challenges 7 MobilityPerception Manipulation “Go get me a beer from the fridge” Stairs Opening a door Sand Eggs Unstructured terrain Where to grasp object Localization Mapping
- 8. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Outline • Introduction • Tools • Switchblade • SkySweeper • Conclusions 8
- 9. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Mechanical Engineering • 3D printing • Multiple materials are here, and more are coming • New generation of CAD tools • TinkerCAD • OpenSCAD • Onshape 9
- 10. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Electrical Engineering • Eagle CAD • SparkFun library • Fritzing • Unique breadboard view • CircuitMaker • powered by Altium 10
- 11. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Electrical Engineering • Voxel8 Multi-material 3D printer • Autodesk Project Wire 11
- 12. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 12
- 13. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Funding • Bootstrapping • Accelerators/Incubators • Increasing number of hardware accelerators 13
- 14. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Crowdfunding • Just posting on Kickstarter does not guarantee success! 14
- 15. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Crowdfunding 15 from Cyril Ebersweiler’s Hardware trends 2015 slideshare http://www.slideshare.net/haxlr8r/hardware-trends-2015 or search: slideshare hardware trends
- 16. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 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 16 atan2 1/s Low Pass High Pass s Accelerometer Gyroscope Encoder + + ++ ++ ˙ ˙✓ ✓ µGHP = 1/!c 1/!c + h , µALP = h 1/!c + h
- 17. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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) 17 A ARF B AFR BFR BRF AR BR BR AF AF BF BF AR ARR BFF M = 2!h CPR ⇡
- 18. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Lagrangian Dynamics • Powerful dynamics formulation • Apply constraints with Lagrange multiplier • Broadly applicable to a large class of robotic systems • Can be applied programmatically 18 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)T M(q)¨q + S(q)T F(q, ˙q) = S(q)T Q
- 19. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Tools Lagrangian Dynamics 19 ˙q = S⌫, ¨q = S ˙⌫, ST M(q)S ˙⌫ + ST F(q, ˙q) = ST Q ˙⌫ = [ST M(q)S] 1 ST [Q F(q, ˙q)] ¨q = S[ST M(q)S] 1 ST [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] 1 ST [BZ( ˙q) + F(q, ˙q)] ◆ (x) = ✓ 0n⇥nu ¯ S[ST M(q)S] 1 ST B⌃ ◆
- 20. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 20 ˙⌫ = [ST M(q)S] 1 ST {B[⌃u Z( ˙q)] F(q, ˙q)} = 0nr⇥1 ST {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⇤ )
- 21. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 21 ˙˜x =A˜x + B(˜u + u⇤ ) A = f(˜x + x⇤ ) ˜x ˜x=0 , B = (˜x + x⇤ ) ˜x=0 ˙⇠ =C˜x, ¯x = ✓ ˜x ⇠ ◆ , ˙¯x = A¯x + B(˜u + u⇤ ) A = A 02n⇥nu C 0ni⇥nu , B = B 0ni⇥nu ¯xk+1 =F ¯xk + G(˜uk + u⇤ ) F =eAh , G = Z h 0 eA⌘ Bd⌘ u =K ✓ x x⇤ ⇠ ◆ + u⇤
- 22. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Outline • Introduction • Tools • Switchblade • SkySweeper • Conclusions 22
- 23. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 23
- 24. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 24 θ α ϕ LT LC rmT mC w mS X Yρ w = r( ↵) ⇢(⇡/2 ↵) P = µkmgr sin ↵ ( ˙ ˙↵) cT ( ˙↵ ˙✓) P ˙q = 0 B B @ 0 µkmgr sin ↵ · sgn( ˙ ˙↵) µkmgr sin ↵ · sgn( ˙ ˙↵) cT · sgn( ˙↵ ˙✓) cT · sgn( ˙↵ ˙✓) 1 C C A , q = 0 B B @ w ↵ ✓ 1 C C A
- 25. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 25
- 26. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Switchblade 26
- 27. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Switchblade Perching • Friction compensator improves performance • Oscillation is due to stiction • Performance limited by mass distribution and friction 27 0 1 2 3 4 5 6 7 8 9 10 −0.5 0 0.5 1 1.5 2 T im e (sec) Angle(rad) φ α θ φ∗ 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 im e (sec) φ−α(rad) 0 1 2 3 4 5 6 7 8 9 10 −1 −0.5 0 0.5 1 T im e (sec) ˙φ−˙α(rad/sec) Ex p erim ental a S = 0 Ex p erim ental a S = 0.06 Sim ulation a S = 0 Sim ulation a S = 0.06 φ∗ − α ∗ θ α ϕ LT LC rmT mC w mS X Yρ
- 28. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Outline • Introduction • Tools • Switchblade • SkySweeper • Conclusions 28
- 29. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 29
- 30. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 30
- 31. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 31
- 32. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 32
- 33. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 𝜃 𝜶 x y 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 33 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
- 34. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 𝜃+π-𝜶 > 1.9 𝜃+π-𝜶 < 1.0 State 0: Open Clamp 1: Pivoting Clamp 2: Rolling u = -0.65 State 1: Close Clamp 1: Rolling Clamp 2: Pivoting u = 0.40 State 8: Swing 1 Clamp 1: Pivoting Clamp 2: Open u = -0.20 State 9: Charge 2 Clamp 1: Pivoting Clamp 2: Pivoting u = 1 Cable in grasp of clamp 2 State 7: Charge 1 Clamp 1: Pivoting Clamp 2: Pivoting u = -1 𝜶-γ > 1 State 10: Swing 2 Clamp 1: Open Clamp 2: Pivoting u = 0.20 𝜶-γ < -1 Cable in grasp of clamp 1 34 State 5: Swing Clamp 1: Pivoting Clamp 2: Open u = 0.7t*sin(π t) State 6: Hold Clamp 1: Pivoting Clamp 2: Pivoting u = 0 Cable in grasp of clamp 2 Inchworm Swing-Up Backflip
- 35. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 35
- 36. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 SkySweeper Inchworm 36
- 37. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 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 37 0 0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 t(s) LinkSeparation 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) SpringDeflection α−γ(rad) Simulation Experimental
- 38. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 SkySweeper Swing-Up 38
- 39. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 SkySweeper Backflip 39
- 40. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Outline • Introduction • Tools • Switchblade • SkySweeper • Conclusions 40
- 41. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Conclusions Nick’s Rules of Robotics 41 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.
- 42. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Conclusions Nick’s Rules of Robotics 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. 42
- 43. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Conclusions Nick’s Rules of Robotics 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. 43
- 44. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Conclusions Nick’s Rules of Robotics 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. 44 ServoCity.com clamping hub
- 45. UCSD Coordinated Robotics Lab Nick Morozovsky Mar 17, 2015 Conclusions Acknowledgments • Advisor: Professor Thomas Bewley • Chris Schmidt-Wetekam, Andrew Cavender • Members of the Coordinated Robotics Lab at UCSD 45