Jason K. Moore

Modeling the Manually Controlled Bicycle

A control-theoretic model of the bicycle rider is developed. The model has its origins in pilot modeling efforts previously reported in the literature. A handling-quality metric that was employed in pilot/vehicle analysis is adopted for use in estimating the task-independent handling qualities of bicycles. The resulting model is parameterized by five gains, two fixed second-order filters, and a preview time. Analysis and computer simulation of the rider/bicycle system are undertaken using six linear models of existing bicycles at three different velocities. The riders task consisted of a 2-m lane-change maneuver and return. Lane tracking performance was comparable for all bicycles at each velocity. Distinct variations in estimated handling-quality levels were evident in the analysis that indicated that bicycle velocities, rather than differences in the bicycles themselves, dominated the handling-quality predictions. A brief discussion of a rider control model for hands-free riding and a possible approach for model identification concludes this paper.

SOME OBSERVATIONS ON HUMAN CONTROL OF A BICYCLE

The purpose of this study is to identify human control actions in normal bicycling. The task under study is the stabilization of the mostly unstable lateral motion of the bicycle-rider system. This is done by visual observation of the rider and measuring the vehicle motions. The observations show that very little upper-body lean occurs and that stabilization is done by steering control actions only. However, at very low forward speed a second control is introduced to the system: knee movement. Moreover, all control actions are performed at the pedaling frequency, whilst the amplitude of the steering motion increases rapidly with decreasing forward speed.Copyright

A METHOD FOR ESTIMATING PHYSICAL PROPERTIES OF A COMBINED BICYCLE AND RIDER

A method is presented to estimate and measure the geometry, mass, centers of mass and the moments of inertia of a typical bicycle and rider. The results are presented in a format for ease of use with the benchmark bicycle model [1]. Example numerical data is also presented for a typical male rider and city bicycle.

Rider control identification in bicycling using lateral force perturbation tests

A model describing rider control while steering and stabilizing a bicycle has been developed. Experimental data were obtained from riding a bicycle on a narrow treadmill while perturbing balance with impulsive forces at the seat post. The experiments were conducted at 2–7 m/s covering both the stable and the unstable forward speed range. Bicycle and rider mechanics have been modeled using the Whipple bicycle model extended with the rider inertia. A rider control model applying steering torque at the handle bars has been developed exploring potential feedback of visual, vestibular and arm proprioceptive cues. The identified rider control parameters, after model reduction, stabilize the system and mimic realistic rider control behavior. The feedback gains of this control model were used to identify the specific optimal control linear-quadratic regulator (LQR) cost function which the rider was using to control the bicycle. The identified cost functions indicate that at low speed the rider minimizes his control effort and at high speed he minimizes the heading error.

Constrained Multibody Dynamics With Python: From Symbolic Equation Generation to Publication

Symbolic equations of motion (EOMs) for multibody systems are desirable for simulation, stability analyses, control system design, and parameter studies. Despite this, the majority of engineering software designed to analyze multibody systems are numeric in nature (or present a purely numeric user interface). To our knowledge, none of the existing software packages are 1) fully symbolic, 2) open source, and 3) implemented in a popular, general, purpose high level programming language. In response, we extended SymPy (an existing computer algebra system implemented in Python) with functionality for derivation of symbolic EOMs for constrained multibody systems with many degrees of freedom. We present the design and implementation of the software and cover the basic usage and workflow for solving and analyzing problems. The intended audience is the academic research community, graduate and advanced undergraduate students, and those in industry analyzing multibody systems. We demonstrate the software by deriving the EOMs of a N-link pendulum, show its capabilities for LATEX output, and how it integrates with other Python scientific libraries allowing for numerical simulation, publication quality plotting, animation, and online notebooks designed for sharing results. This software fills a unique role in dynamics and is attractive to academics and industry because of its BSD open source license which permits open source or commercial use of the code. ∗Address all correspondence to this author INTRODUCTION There are many dynamic systems which can be better or more effectively studied when their EOMs are accessible in a symbolic form. For equations that may be visually inspected (i.e., of reasonable length), symbolics are generally preferable because the interrelations of the variables and constants can give clear understanding to the nature of the problem without the need for numerical simulation. Many classic problems fit this category, such as the mass-spring-damper, double pendulum, rolling disc, rattleback, and tippy-top. The benefits of symbolic equations of motion are not limited to these basic problems though. Larger, more complicated multibody systems can also be studied more effectively when the equations of motion are available symbolically. Advanced simplification routines can sometimes reduce the length of the equations such that they are human readable and the intermediate derivation steps are often short enough that symbolic checks can be used to validate the correctness. Furthermore, the symbolic form of the EOMs often evaluate much faster than their numerical counterparts, which is a significant advantage for real time computations. Problems in biomechanics, spacecraft dynamics, and single-track vehicles have all been successfully studied using symbolic EOMs. Having the symbolic equations of motion available permits numerical simulation, but also allows for a more mathematical study of the system in question. System behavior can be studied parametrically by examining coefficients in the differential equations. This includes symbolic expressions for equiProceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA

Rider Optimal Control Identification in Bicycling

Rider control in bicycling is modeled by first adding the rider as a passive mechanism to the Whipple bicycle model. Next, for the rider control model a linear PID controller with and without delay is assumed, where the control inputs are the bicycle roll and steer angle with their higher derivatives, and the control output is the action-reaction steer torque applied by the rider at the handle bars. The experimental data is obtained from riding a bicycle on a narrow treadmill while applying an intermitted lateral perturbation by means of an impulse force applied at the seat post. The experiments are conducted in both the stable and the unstable forward speed range. After some filtering, a parametric control model is fitted to the data. Finally, the gains of this control model are used to identify the specific optimal control LQR cost function which the rider is using to control the bicycle on the treadmill at the various forward speeds.

skijumpdesign: A Ski Jump Design Tool for Specified Equivalent Fall Height

Over the past three decades an evolution has occurred toward freestyle skiing and snowboarding involving aerials in terrain parks at ski resorts hosting dedicated jumping features. Today more than 95% of US ski resorts have such jumps but these rarely, if ever, involve formal or detailed design or engineering. Although usually tested and modified before being opened to the public, they are often simply fabricated based on the past experience of the builder in jump construction. Together with the increase in these jumps has come a concomitant increase in injuries and their very high social costs. Although omitted here, the voluminous epidemiology and financial effects of these injuries are covered in detail in references (Hubbard, 2009, McNeil, Hubbard, & Swedberg (2012), Levy, Hubbard, McNeil, & Swedberg (2015), Petrone, Cognolato, McNeil, & Hubbard (2017)).

Estimating Parameters of the Structural Pilot Model from Simulation Tracking Data

The research to be described presents a preliminary analysis of a method for identifying a limited set of parameters from the Structural Pilot Model using data from human-in-the loop simulation tasks. Four simple controlled-element dynamics are chosen requiring pilot compensation ranging from lags to firstorder leads. Then tracking data for longitudinal control of a model of a large transport aircraft is analyzed for a cruise flight condition. In all cases, the Structural Pilot Model parameters are limited to those in the proprioceptive feedback loop and the forward loop operating on visually displayed error. These parameter values determine fundamental pilot compensation and open-loop crossover frequencies. Using the identified pilot model parameters, Handling Qualities Sensitivity Functions are created for the estimation of vehicle handling qualities levels.