Towards a maximally-robust self-balancing robotic bicycle without reaction-moment gyroscopes nor reaction wheels

Transcription

1 Towards a maximally-robust self-balancing robotic bicycle without reaction-moment gyroscopes nor reaction wheels Arundathi Sharma, Shihao Wang, Yu Meng Zhou, etc, (students) Andy Ruina (project advisor) Cornell, Mechanical Engineering BMD 2016, Milwaukee, WI. Sept 21

2 Summary Goal make robotically-stabilized bike really stable w/ some navigation Features No reaction wheels No reaction moment gyros Balance only by steer control and speed control Why? Self-driving bike (e.g., Google-bike Youtube parody) Learn about balance control (for imperfect systems) Steer-by-wire bike is a better bike? (like Schwab et al) To study human control (e.g. Moore & Schwab)

3 Related attempts with and without reaction wheels or reaction-moment gyros. (next few slides)

4 Auto-balancing with reaction-moment gyros Fiction: Two Boys in a Jyrocar (1911) Shilovsky Gyrocar (1912) Balance by reaction-gyroscope 2.75 tons, large turning radius

5 With reaction moment gyro 6 weight of typical electric motorcycle Lit Motors C-1 March,

6 George Mason With reaction wheel Technische Universität, Berlin (Schmidt) George Mason, 2009 (undergrad project) Can t turn Handles small disturbances Can t turn Handles disturbances Tested for balance while motionless Milliken/CALSPAN Reaction-wheel Motorcycle ~1980 Doug Milliken (here)

7 Our self-imposed rules No reaction-moment gyroscopes Heavy and unwieldy Don t inform us about human balance No reaction wheels Also heavy, expensive and energy intense We want our bicycle to control itself like a person (mostly) does, with steering.

8 Just steering, no gyros or reaction wheels. Mahanakorn University of Technology (Thailand) Stable only at high speeds Can t make sharp turns Can t do a track stand Mahanakorn University of Technology,

9 Just steering (cont d) TU Delft Has rotary encoder, lean gyro Turns into fall Steer rate = c*(lean rate) Oscillations in straight-line motion Can t track stand Delft (2010)

10 Just steering (cont d) Luke Peterson, UC Davis Balances at 1m/s Does not track stand Does not self-navigate UC Davis (2013)

11 Summary of others attempts (without reaction stuff): stable only at high speeds not navigationally autonomous In contrast, we want low-speed stability (All the way to track-stand) Navigation (go between GPS way points) (e.g., low-speed ride around Cornell paths)

12 Physical robot: Dahon (donated) folding bicycle, Motors: rear wheel, steering, kick stand (2 sides). Sensors: GPS, compass, IMU (lean, lean rate), steering encoder, rear wheel encoder. Electronics: Arduino Due, RC (over-ride).

13 Model CBAD (for designing and testing controllers) Primitive model: (Boussinesq, Bourlet, Getz & Marsden) All mass at point G; All inertias = 0; Head angle AD = 0; Wheel radius (C & D)= 0; No steering dynamics (steer angle δ controlled); Simplification of TMS bike. Note: δ α

14 Corrected geometry Error goes back to 1800s. Only important for large lean θ. [Essence of old error: Front wheel trackline deviates α from wheelbase line by more than the steer angle δ. α>δ ]

15 Governing equations Non-linear lean Φ equation: g = gravity h = height of Center of Mass l = wheelbase length b = fore-aft position of CoM (b<l) Linear lean Φ equation: Fall acceleration due to: gravity, going in circles, parallel steering Controls: speed v (rear wheel) steer u = dδ/dt are controls. Strictly non-linear terms

16 Governing equations Non-linear lean Φ equation: g = gravity h = height of Center of Mass l = wheelbase length b = fore-aft position of CoM (b<l) Linear lean Φ equation: Allows track stand. If δ 0 then dv/dt has authority over balance. Fall acceleration due to: gravity, going in circles, parallel steering Controls: speed v (rear wheel) steer u = dδ/dt are controls. Strictly non-linear terms

17 If you control steering directly (velocity, not torque), Our model is similar to full Whipple model. simple model seems good enough for controller testing. Lean angle disturbance recovery Whipple & Point mass (initial disturbance ɸ = π/8, stabilizes at zero lean)

18 Control approach v1.0: For now, control is linear Pole placement finds set of linearly stable gains. initial search space Control law: command = steer rate = u saturates at 10rad/s φ = lean angle δ = steer angle (note: no steer dynamics)

19 Controller Selection Tested ~100,000 controllers over set of 4 initial states (ICs): 4 rows are 4 ICs Each gain set has a score:

20 Best controller selected: Ten lowest-score gain sets simulated with Errors in lean and steer angle sensor (-/+0.02rad, -/+0.04rad) Varied bicycle geometry. (l: -0.2/+0.5m; h: -0.1/+0.2m) Errors in actuator: 土5% Two gain sets never fell. The lowest scoring one: (With our consistent units) Best gain set recovers from disturbances (one at a time): Lean angle: 41 Lean rate: 2.5rad/s ( 143 /s ) Steer angle: 60 Pretty good balance :-)

21 Yaw and path following: Used same balance controller, modified: Control (see figure): δ saturates at 士45 ; -π<ө<π Gains optimized intuitively from simulations

22 Navigation Test (triangle path) Desired path: 30m:40m:50m triangle Bike path: Starts in wrong direction Starts turn 4m before corners This is v1, still improving (Video)

23 Project status Debugging sensors, actuators, and core control code (ongoing) Next steps (next two months): Implement and test linear control for balance Implement and test way-point navigation (using GPS) Test supposedly-more-robust non-linear controllers (state-based) Debugging whole system for robustness December 1 goal: * Cornell paths without falling * Track stand

24 Challenges/goals Longest time in track-stand Longest time in motion w/ no touch down or refueling Slowest stable motion (w/o reaction stuff) Wildly robust disturbance rejection Thanks.