Scholarly article on topic 'Low-power, modular, wireless dynamic measurement of bicycle motion'

Low-power, modular, wireless dynamic measurement of bicycle motion Academic research paper on "Medical engineering"

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{"Bicycle dynamics" / Instrumentation / "Wireless data acquisition"}

Abstract of research paper on Medical engineering, author of scientific article — Dale L. Peterson, Jason K. Moore, Danique Fintelman, Mont Hubbard

Abstract A low power, light-weight, and modular system of sensors and data acquisition hardware was developed to measure the configuration, velocities, and accelerations of a bicycle. Measurement of angular velocity of the bicycle frame, acceleration of three points fixed to the frame, steer angle, and wheel spin rates is implemented. Measurements will be compared with dynamic models of the bicycle and human rider in order to assess model fidelity. In this way, we hope to (1) better understand how humans control bicycles, and (2) pave the way for bicycle design improvements based on quantitative and relevant dynamic measurements.

Academic research paper on topic "Low-power, modular, wireless dynamic measurement of bicycle motion"

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Procedía Engineering 2 (2010) 2949-2954

Procedía Engineering

www.elsevier.com/locate/procedia

Low-power, modular, wireless dynamic measurement of bicycle

motion

Dale L. Petersona*, Jason K. Moorea, Danique Fintelmana1, Mont Hubbarda

aSports Biomechanics Lab, University of California Davis, Davis, CA, 95616, USA

Abstract

A low power, light-weight, and modular system of sensors and data acquisition hardware was developed to measure the configuration, velocities, and accelerations of a bicycle. Measurement of angular velocity of the bicycle frame, acceleration of three points fixed to the frame, steer angle, and wheel spin rates is implemented. Measurements will be compared with dynamic models of the bicycle and human rider in order to assess model fidelity. In this way, we hope to 1) better understand how humans control bicycles, and 2) pave the way for bicycle design improvements based on quantitative and relevant dynamic measurements. © 2010 Published by Elsevier Ltd. Keywords:

bicycle dynamics, instrumentation, wireless data acquisition

1. Introduction

Accurate measurement of the bicycle parameters and dynamic variables is crucial for experimental validation of dynamic models. They include two angles (lean and steer), six angular rates (3 body-fixed rates of the frame, steer rate, and the two wheel rates), and the time derivatives of these six angular rates. By measuring or estimating each of these quantities, direct comparison with the equations of motion is possible.

A significant challenge of this measurement task is to allow for a small, unobtrusive solution which doesn't interfere with normal cycling or affect the dynamics significantly, yet is still capable of accurate measurement. Various approaches for experimental validation of bicycle models have been taken. In a CALSPAN study by Rice and Roland [1], the design parameters associated with the bicycle motion in the longitudinal plane were studied by performing a variety of typical bicycle maneuvers. One of the main conclusions was that short wheelbases and front

* Corresponding author

Email address: dlpeterson@ucdavis.edu (Dale L. Peterson) 1Visiting intern at Sports Biomechanics Laboratory, January - April 2010

1877-7058 © 2010 Published by Elsevier Ltd. doi:10.1016/j.proeng.2010.04.093

brakes can be hazardous. In another CALSPAN study by Roland and Lynch [2], extensive efforts were made to develop a rider control model, perform bicycle tire testing, develop a computer graphics simulation, and to perform measurements of the bicycle during common maneuvers. Steer angle, roll angle, lateral frame acceleration, and forward speed were measured. Kooijman et al. [3] compared weave modes estimated from time histories of measured roll rate to weave modes predicted by thoroughly verified linearized equations of motion [4], and found that the model eigenvalues matched experimental ones reasonably well for low speed maneuvers (0 - 6 m/s).

The bicycle used in our experiments serves two purposes: 1) to validate dynamic bicycle models with both rigidly attached rider (as in [4]) and permitted to lean their upper body (as in [5, 6]); 2) to develop and validate dynamic control models of the human rider. The former purpose requires experiments be conducted without a human rider, so some basic stabilization and tracking control capabilities are needed, but autonomous operation is not. Here, actuation will be provided by use of electric motors for steer, rider lean (mimicked by an inverted pendulum on bicycle frame), and the rear wheel. The latter purpose requires that the bicycle be humanly rideable.

With the advent of smaller dynamic measurement technologies, it is now possible for a much more detailed measurement of the dynamic bicycle state. For example, 3-axis accelerometers, weighing less than 2.0 grams, with built-in 12-bit analog-to-digital conversion, capable of measuring ±2.0g are now available for less than $10 US. The case is similar for rate gyroscopes and optical encoders to measure the angular velocities of the frame, fork, and wheels. These measurements will allow for detailed validation of mathematical models through direct comparison of measurement with simulation. For example, by accurately measuring the wheel spin rate of both wheels, the hypothesis that the wheels roll without slip can be quantitatively tested by determining to what degree the measurements satisfy the nonholonomic constraints associated with the no-slip rolling assumptions. These types of validations have yet to be performed in the bicycle research community.

2. Materials and Methods

2.1. Overview

The measurement system is implemented with sensors connected to a two wire (i2C) sensor network; each sensor can be considered a slave device which responds to the commands of the master. Analog to digital conversion is performed immediately adjacent to each analog sensor to minimize effects of noise, and the digital representation of the measured signal is then made available on the i2C network in the form of a 2-byte integer. An Arduino [7] electronics prototyping board with an AVR micro controller [8, 7] was used for as the master i2C device and requests measurement from each sensors. Each set of sensor measurements is sent via the Ar-duino serial port to an XBee-PRO®wireless module (Digi International®), which then sends the measurements wirelessly to a PC with a mating XBee-PRO wireless module. The i2C sensor network is capable of 400kbps, while the wireless module is capable of 250kbps. This is more than adequate for our system because even in the case of 32 sensors (we use 20) at 16 bits per sample, a 100Hz sampling frequency would result in a data rate of 51.2kbps, drastically less than the network bandwidth.

Once wirelessly transmitted to the PC, the measurements are read from the serial port into the GUI. This allows for real time visualization of every measurement, and for quick verification

that each sensor is behaving properly. It also allows for the data to be stored to a file for future processing.

The direct measurements we make, along with the number of signals are:

• Body fixed angular velocity of bicycle frame and fork (6)

• Steer angle (1)

• Wheel spin rates (2)

• 3-axis linear accelerations of three points of bicycle frame (9)

• Applied steer torque (1)

• Mimicked rider lean angle, inverted pendulum angle (1) From these 20 measurements, we estimate the following quantities:

• Yaw, roll, pitch (Euler 3-1-2) angles of bicycle frame

• Steer rate, rider lean rate, time derivatives of six angular rates

The lean (roll) of the bicycle frame is the most difficult quantity to measure directly. Optical methods provide high accuracy but tend to be expensive, heavy, and affected by road surface reflectance and camber. Accurate estimation of the lean is possible by means of careful filtering and numerical integration of rate gyroscope signals, as in [9, 10, 11]. This is the approach we take for estimation of the orientation of the bicycle frame in inertial space.

A schematic representation of the bicycle with the inverted pendulum, along with the measurement equipment is shown in Figure 1.

2.2. Steer angle, pendulum angle

Potentiometers were employed to measure the angular displacement of the fork and of the inverted pendulum. 16-bit A/D conversion was employed locally to each potentiometer to minimize noise. The digitized measurement is made available on the i2C bus. With 16-bit A/D, a theoretical resolution of about 0.0006° is possible. However, due to voltage noise levels on the order of 1.0mV, realistic measurement accuracy is about 0.01°, which we found acceptable for our purposes.

2.3. Angular rate measurement

Three single axis MEMS rate gyroscopes (ST Microelectronics, LY510ALH) with a full-scale range of 100°/sec were oriented along perpendicular axes and attached to the bicycle frame. Three measurement axes are the steer axis, an axis normal to the plane of symmetry, and a third orthogonal to the other two. A simple low pass RC filter with 20Hz cutoff frequency was implemented in the rate gyroscope circuit, and the signal was sampled using a 16-bit A/D converter with a maximum sample rate of 860Hz.

The noise rate density a of these sensors impose limits on the attainable measurement resolution. For the particular rate gyroscopes chosen, a = 0.017°/s/ VHz, which yields an RMS noise value of 5.1mV, which corresponds to aresolution of approximately ±0.5°/s.

Pendulum & Motor

36 Volt Battery

Cruise Control

\ I Steer MEMS rate gyro

Steer motor

Torque /

Load Cell V J ^^^ - Steer angle potentionmeter 3-Axis MEMS Rate Gyro

Figure 1: Schematic overview of measurement equipment.

2.4. Wheel spin rates

Reflective two channel optical encoders (Avago Technologies, AEDR-8300-1K) and encoder discs are employed at both wheels to estimate their rates independently. Optical encoders were chosen because of their high accuracy at low speeds, their fast dynamic response, and the fact that they introduce no friction. Wheel spin rate is estimated by counting the number n of clock cycles of period Tc that occur between encoder wheel transitions, of which there are p counts per revolution. The angular rate is estimated as

- 2n_L

eS' p Tcn

For a wheel angular speed u rad / s, the time between encoder transitions is

T, - —

The number of clock counts that occur in this time period is

n = floor

which implies that the relative error is

erel = ■

p Tfoor^)

PWTc floor

The relative speed estimation error, as a function of a>, is bounded by a line of slope Tcp/2n which passes through the origin. This implies a measurement error of less than 0.5% for wheel rates up to 61.4 rad/s (approximately 20 m/s). Additionally, the 16-bit counter used for counting clock cycles allows for speeds as low as 0.03 rad / s, or about 0.01 m / s, implying the lower end of detectable speeds is well below what would be considered rideable.

2.5. Accelerometers

Three 3-axis accelerometers (ST Microelectronics, LIS3LV02DQ) are rigidly attached to three different points on the frame, and their relative positions were measured to within ±1.0mm. When the bike is stationary, the three sensors each act as a tilt sensor which can provide the initial orientation (lean and pitch, with yaw being ignorable and undetectable by a stationary 3-axis accelerometer) of the bicycle before the experiments begin. Given a stationary 3-axis accelerom-eter with three measurement signals ax, ay, az, the magnitude of the gravitational acceleration, lean, and pitch may be calculated as

| g| = ^ + aj + a? (5)

0 = arcsin (ay/| g| ) (6)

8b = arccos |az/||g| - (ay/|g|fjj (7)

This initial angular orientation is then added to the integration of the rate gyroscope signals to give the estimated orientation as the bicycle moves. Initial heading ('yaw') can be taken to be zero since it has no influence on the dynamics.

2.6. Steer Torque

Steer torque was measured by equipping the steer tube of the bicycle fork with strain gauges in a configuration which minimizes the measurement sensitivity to the influences of bending moments. The strain gauge voltage was sampled locally with the same type of 16-bit analog-to-digital converter used for the rate gyroscopes, and this sensor measurement was then made available on the i2C bus.

2.7. Real time GUI

To visualize the sensors signals in real-time and ensure that their readings are meaningful, a GUI tool was was developed using Python and the Qt GUI toolkit. These GUI tools are open source, free, platform independent and widely used for elegant GUI design.

Data collection is started and stopped through the GUI interface, which eliminates the need to 'press go' on a data acquisition device that physically resides on the bicycle. When an experiment is begun, a dialog pops up with a number of fields allowing for the filename and other descriptive information to be entered about the experiment to be performed. Once the experiment is started, data is continuously written to a file, while simultaneously being plotted in real-time. Fields such as the signal mean, the standard deviation, and the sample time are displayed in real-time. During the experiment, the person monitoring the GUI can add comments or notes inside a text box and they will be stored along with the measurement data at the end of the experiment.

The GUI greatly assists in conducting organized experiments where the data is collected and organized in a systematic and consistent fashion.

3. Results

The equipment developed in this effort will be used in the coming months to perform experiments to help validate models of the rider and the bicycle. Currently, the design and construction is still in progress; it is our goal to have a fully functional system by May 2010.

4. Discussion

The advent of low cost yet accurate dynamic measurement technologies, along with readily available and easily programmable micro controllers with wireless communications abilities enables many common mechanical systems to be accurately measured and controlled. With this data acquisition system, we aim to have the most complete and accurate dynamic measurements of the bicycle that have been performed to date. The physical size and weight of our system is drastically smaller, lighter, and more modular than any system, and will pave the way for a more complete understanding of the bicycle and how a human rides it.

5. Acknowledgements

Benny Brown provided guidance in the selection and design of the data acquisition. His electrical engineering knowledge filled many gaps in our knowledge and allowed us to ensure our measurements would be accurate and consistent.

References

[1] R. S. Rice, R. D. Roland, An Evaluation of the Performance and Handling Qualities of Bicycles, Calspan Report VJ-2888-K, Cornell Aeronautical Laboratory, prepared for the National Commission on Product Safety (April 1970).

[2] R. Roland, J. Lynch, Bicycle Dynamics Tire Characteristics and Rider Modeling, Calspan Report YA-3063-K-2, Cornell Aeronautical Labaratory, Inc., Buffalo, NY, USA, prepared for the Schwinn Bicycle Company (March 1972).

[3] J. D. G. Kooijman, A. L. Schwab, J. P. Meijaard, Experimental validation of a model of an uncontrolled bicycle, Multibody System Dynamics 19 (2008) 115-132. doi:10.1007/s11044-007-9050-x.

[4] J. P. Meijaard, J. M. Papadopoulos, A. Ruina, A. L. Schwab, Linearized dynamics equations for the balance and steer of a bicycle: A benchmark and review, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463 (2084) (2007) 1955-1982. doi:10.1098/rspa.2007.1857.

URL http://rspa.royalsocietypublishing.org/content/463/2084/1955.abstract

[5] D. L. Peterson, M. Hubbard, Yaw rate and velocity tracking control of a hands-free bicycle, in: International Mechanical Engineering Congress and Exposition, ASME, Boston, 2008.

[6] A. L. Schwab, J. D. G. Kooijman, J. P. Meijaard, Some recent developments in bicycle dynamics and control, in: A. K. Belyaev, D. A. Indeitsev (Eds.), Fourth European Conference on Structural Control (4ECSC), Institute of Problems in Mechanical Engineering, Russian Academy of Sciences, 2008, pp. 695-702.

[7] Arduino electronics prototyping platform (January 2010). URL http://www.arduino.cc/

[8] Atmel 8-bit avr risc atmega328p (January 2010).

URL http://www.atmel.com/dyn/products/product_card.asp?PN=ATmega328P

[9] I. Boniolo, M. Tanelli, S. Savaresi, Roll angle estimation in two-wheeled vehicles, in: 17th IEEE International Conference on Control Applications, Part of 2008 IEEE Multi-conference on Systems and Control, San Antonio, Texas, USA, 2008, pp. 31-36. doi:10.1109/CCA.2008.4629599.

[10] M. Norgia, I. Boniolo, M. Tanelli, S. Savaresi, C. Svelto, Optical Sensors for Real-Time Measurement of Motorcycle Tilt Angle, IEEE Transactions on Instrumentation and Measurement 58 (5) (2009) 1640-1649. doi:10.1109/TIM.2008.2009421.

[11] I. Boniolo, S. M. Savaresi, M. Tanelli, Roll angle estimation in two-wheeled vehicles, IET Control Theory and Applications 3 (1) (2009) 20-32. doi:10.1049/iet-cta:20080052.