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M.M. Reijne
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Minimum-time optimisation has been used extensively in motorsports, such as Formula One racing. Using minimum-time optimisation, the ideal racing line as well as control strategies such as braking strategies can be found. This is interesting, as Reijne et al have shown that cyclists apply diverse strategies, specifically during a descent [1]. With minimum-time optimisation, it is possible to compare a riders performance to the theoretically optimal performance. The results from such optimisations can be used to help with training, as well as improve and test equipment design.
This work describes a free-trajectory steady motion control optimisation for the descent of elite cyclists. The prediction of the individual descent performance was formulated as an optimal control problem and solved with a direct approach to finding optimal cornering and braking strategies that yield the shortest descent time. While the state equations were kept simple (3 variables only), more elaborated performance limits were represented by g-g diagrams. Such diagrams represent the longitudinal, lateral, and combined acceleration limits for cyclists. A method to numerically derive g-g diagrams for cyclists driving on 3D tracks was designed. In this method, a tire model, power limit, and steady motion equations for a cyclist are used to determine the control space. The bicycle and cyclist are modeled as a single rigid body, the tire friction model is simplified as a friction circle, and the wind speed is considered to be zero at all times. As for the 3D road geometry effects, all possible effects are considered in the method, except lateral road curvature. The resulting method
provides g-g diagrams as a function of 8 local geometry and state variables.
The optimisation model was tested against the velocity and trajectory output data measured on Team Sunweb professional cyclists at the L218 descent in Germany. The resulting trajectory was similar to the trajectory ridden by elite cyclists. The velocity profile showed large differences, which are a result of a combination of inaccurate track data, differences in friction coefficient estimation, and safety margins applied by the cyclists. The results show that descent performance can be improved, as even when adhering to safety margins harder braking is possible. Overall, the model responds as expected to changes in track, environment, and bicycle/rider parameters.
Steps can be made towards better implementation of the g-g diagrams in the minimum-time optimisation. Furthermore, a more accurate tire model and power model can improve the model and extend its applications. The presented model can be used for qualitative descent analyses, and facilitate the training of elite cyclists.
[1] A.L. Schwab, M.M. Reijne, D.J.J. Bregman, Measuring and comparing descend in elite race cycling with a perspective on real-time feedback for improving individual performance. In Multidisciplinary Digital Publishing Institute Proceedings, volume 2, page 262, 2018.
...
This work describes a free-trajectory steady motion control optimisation for the descent of elite cyclists. The prediction of the individual descent performance was formulated as an optimal control problem and solved with a direct approach to finding optimal cornering and braking strategies that yield the shortest descent time. While the state equations were kept simple (3 variables only), more elaborated performance limits were represented by g-g diagrams. Such diagrams represent the longitudinal, lateral, and combined acceleration limits for cyclists. A method to numerically derive g-g diagrams for cyclists driving on 3D tracks was designed. In this method, a tire model, power limit, and steady motion equations for a cyclist are used to determine the control space. The bicycle and cyclist are modeled as a single rigid body, the tire friction model is simplified as a friction circle, and the wind speed is considered to be zero at all times. As for the 3D road geometry effects, all possible effects are considered in the method, except lateral road curvature. The resulting method
provides g-g diagrams as a function of 8 local geometry and state variables.
The optimisation model was tested against the velocity and trajectory output data measured on Team Sunweb professional cyclists at the L218 descent in Germany. The resulting trajectory was similar to the trajectory ridden by elite cyclists. The velocity profile showed large differences, which are a result of a combination of inaccurate track data, differences in friction coefficient estimation, and safety margins applied by the cyclists. The results show that descent performance can be improved, as even when adhering to safety margins harder braking is possible. Overall, the model responds as expected to changes in track, environment, and bicycle/rider parameters.
Steps can be made towards better implementation of the g-g diagrams in the minimum-time optimisation. Furthermore, a more accurate tire model and power model can improve the model and extend its applications. The presented model can be used for qualitative descent analyses, and facilitate the training of elite cyclists.
[1] A.L. Schwab, M.M. Reijne, D.J.J. Bregman, Measuring and comparing descend in elite race cycling with a perspective on real-time feedback for improving individual performance. In Multidisciplinary Digital Publishing Institute Proceedings, volume 2, page 262, 2018.
...
Minimum-time optimisation has been used extensively in motorsports, such as Formula One racing. Using minimum-time optimisation, the ideal racing line as well as control strategies such as braking strategies can be found. This is interesting, as Reijne et al have shown that cyclists apply diverse strategies, specifically during a descent [1]. With minimum-time optimisation, it is possible to compare a riders performance to the theoretically optimal performance. The results from such optimisations can be used to help with training, as well as improve and test equipment design.
This work describes a free-trajectory steady motion control optimisation for the descent of elite cyclists. The prediction of the individual descent performance was formulated as an optimal control problem and solved with a direct approach to finding optimal cornering and braking strategies that yield the shortest descent time. While the state equations were kept simple (3 variables only), more elaborated performance limits were represented by g-g diagrams. Such diagrams represent the longitudinal, lateral, and combined acceleration limits for cyclists. A method to numerically derive g-g diagrams for cyclists driving on 3D tracks was designed. In this method, a tire model, power limit, and steady motion equations for a cyclist are used to determine the control space. The bicycle and cyclist are modeled as a single rigid body, the tire friction model is simplified as a friction circle, and the wind speed is considered to be zero at all times. As for the 3D road geometry effects, all possible effects are considered in the method, except lateral road curvature. The resulting method
provides g-g diagrams as a function of 8 local geometry and state variables.
The optimisation model was tested against the velocity and trajectory output data measured on Team Sunweb professional cyclists at the L218 descent in Germany. The resulting trajectory was similar to the trajectory ridden by elite cyclists. The velocity profile showed large differences, which are a result of a combination of inaccurate track data, differences in friction coefficient estimation, and safety margins applied by the cyclists. The results show that descent performance can be improved, as even when adhering to safety margins harder braking is possible. Overall, the model responds as expected to changes in track, environment, and bicycle/rider parameters.
Steps can be made towards better implementation of the g-g diagrams in the minimum-time optimisation. Furthermore, a more accurate tire model and power model can improve the model and extend its applications. The presented model can be used for qualitative descent analyses, and facilitate the training of elite cyclists.
[1] A.L. Schwab, M.M. Reijne, D.J.J. Bregman, Measuring and comparing descend in elite race cycling with a perspective on real-time feedback for improving individual performance. In Multidisciplinary Digital Publishing Institute Proceedings, volume 2, page 262, 2018.
This work describes a free-trajectory steady motion control optimisation for the descent of elite cyclists. The prediction of the individual descent performance was formulated as an optimal control problem and solved with a direct approach to finding optimal cornering and braking strategies that yield the shortest descent time. While the state equations were kept simple (3 variables only), more elaborated performance limits were represented by g-g diagrams. Such diagrams represent the longitudinal, lateral, and combined acceleration limits for cyclists. A method to numerically derive g-g diagrams for cyclists driving on 3D tracks was designed. In this method, a tire model, power limit, and steady motion equations for a cyclist are used to determine the control space. The bicycle and cyclist are modeled as a single rigid body, the tire friction model is simplified as a friction circle, and the wind speed is considered to be zero at all times. As for the 3D road geometry effects, all possible effects are considered in the method, except lateral road curvature. The resulting method
provides g-g diagrams as a function of 8 local geometry and state variables.
The optimisation model was tested against the velocity and trajectory output data measured on Team Sunweb professional cyclists at the L218 descent in Germany. The resulting trajectory was similar to the trajectory ridden by elite cyclists. The velocity profile showed large differences, which are a result of a combination of inaccurate track data, differences in friction coefficient estimation, and safety margins applied by the cyclists. The results show that descent performance can be improved, as even when adhering to safety margins harder braking is possible. Overall, the model responds as expected to changes in track, environment, and bicycle/rider parameters.
Steps can be made towards better implementation of the g-g diagrams in the minimum-time optimisation. Furthermore, a more accurate tire model and power model can improve the model and extend its applications. The presented model can be used for qualitative descent analyses, and facilitate the training of elite cyclists.
[1] A.L. Schwab, M.M. Reijne, D.J.J. Bregman, Measuring and comparing descend in elite race cycling with a perspective on real-time feedback for improving individual performance. In Multidisciplinary Digital Publishing Institute Proceedings, volume 2, page 262, 2018.
Statistics show that cycling accidents have the biggest (and increasing) contribution to the overall number of hospital visits related to traffic accidents in the Netherlands. In the majority of these cycling accidents, no other road users are involved. Because the majority of the cycling accidents are so-called single vehicle accidents, understanding the control behaviour of the cyclist can spark new insight in to effective preventive measures. This thesis aims to achieve that by reviewing the current state-of-the-art in bicycle-rider control research and subsequently proposing a new rider control model that is developed using system identification techniques. The results of a literature review are used to propose a novel bicycle-rider control model structure that includes realistic human neural and cognitive characteristics to predict control behaviour for stabilizing a bicycle. Sensory integration is modelled with a Kalman filter, and human control and prediction capabilities are mimicked with a Linear-Quadratic-Regulator (LQR) and Tapped-Delay-Line predictor, respectively. Human neuromuscular dynamics are included in the model structure in the form of a second order filter and the bicycle dynamics are modelled with the linear Whipple bicycle model. Two different experimental data sets during which cyclists are laterally (roll) perturbed on instrumented bicycles are used: one collected at the UC Davis on both a horse treadmill and in a sports pavilion and the other collected at the TU Delft on a public cycling path (without other road users). The human steer response to the perturbation is separated from other effects caused by unknown disturbances and noise with a non-parametric Finite-Impulse-Response model. A structured system identification approach is used to determine the final free parameter set that approximates the non-parametric model in the best way possible. The data sets are split in a train set and a test set. The model structure is fitted to the train set. The predictive performance is verified by applying the resulting model to the test set. For the UC Davis data, the resulting model has one rider dependent parameter that describes human bicycle-balancing control behaviour for the entire evaluated forward velocity range (2-8 m/s). This parameter is the weight placed on the roll angle in the LQR control algorithm. The single-run training performance in terms of Variance-Accounted-For (VAF) with the non-parametric model reaches up to 97 %. Test performance incurred a VAF drop, on average, of around 10 %. The steer responses of the TU Delft experiment can be predicted with a model that has two rider dependent parameters: the weights placed on the roll angle and roll rate in LQR control algorithm. Training performance reaches up till 83 % and test performance incurred a VAF drop, on average, of around 7%. Promising future directions are the inclusion of a passive rider model to further increase the fidelity of the model. The investigation of the stability margins of the proposed bicycle-rider controller and their sensitivity to bicycle design and/or human sensory and cognitive decline can lead to tailored measures to reduce the injury rate among cyclists.
...
Statistics show that cycling accidents have the biggest (and increasing) contribution to the overall number of hospital visits related to traffic accidents in the Netherlands. In the majority of these cycling accidents, no other road users are involved. Because the majority of the cycling accidents are so-called single vehicle accidents, understanding the control behaviour of the cyclist can spark new insight in to effective preventive measures. This thesis aims to achieve that by reviewing the current state-of-the-art in bicycle-rider control research and subsequently proposing a new rider control model that is developed using system identification techniques. The results of a literature review are used to propose a novel bicycle-rider control model structure that includes realistic human neural and cognitive characteristics to predict control behaviour for stabilizing a bicycle. Sensory integration is modelled with a Kalman filter, and human control and prediction capabilities are mimicked with a Linear-Quadratic-Regulator (LQR) and Tapped-Delay-Line predictor, respectively. Human neuromuscular dynamics are included in the model structure in the form of a second order filter and the bicycle dynamics are modelled with the linear Whipple bicycle model. Two different experimental data sets during which cyclists are laterally (roll) perturbed on instrumented bicycles are used: one collected at the UC Davis on both a horse treadmill and in a sports pavilion and the other collected at the TU Delft on a public cycling path (without other road users). The human steer response to the perturbation is separated from other effects caused by unknown disturbances and noise with a non-parametric Finite-Impulse-Response model. A structured system identification approach is used to determine the final free parameter set that approximates the non-parametric model in the best way possible. The data sets are split in a train set and a test set. The model structure is fitted to the train set. The predictive performance is verified by applying the resulting model to the test set. For the UC Davis data, the resulting model has one rider dependent parameter that describes human bicycle-balancing control behaviour for the entire evaluated forward velocity range (2-8 m/s). This parameter is the weight placed on the roll angle in the LQR control algorithm. The single-run training performance in terms of Variance-Accounted-For (VAF) with the non-parametric model reaches up to 97 %. Test performance incurred a VAF drop, on average, of around 10 %. The steer responses of the TU Delft experiment can be predicted with a model that has two rider dependent parameters: the weights placed on the roll angle and roll rate in LQR control algorithm. Training performance reaches up till 83 % and test performance incurred a VAF drop, on average, of around 7%. Promising future directions are the inclusion of a passive rider model to further increase the fidelity of the model. The investigation of the stability margins of the proposed bicycle-rider controller and their sensitivity to bicycle design and/or human sensory and cognitive decline can lead to tailored measures to reduce the injury rate among cyclists.
One Step At a Time
Newly Proposed Gait Event Detection Using Position Benchmarked Against Existing Acceleration-Based Methods
Gait event detection allows for insight into one’s gait pattern, an invaluable aid in rehabilitation. Current methods often rely on measured acceleration and rarely on position measurements [3]–[6]. In this paper we propose 4 novel gait detection methods based on the position of the Center of Mass (one approach being causal and thus suitable for real-time use) and compare them to 4 existing state-of-the-art acceleration- based methods. All algorithms are benchmarked on an existing data set (overground walking, 23 participants, 1772 steps), comparing the detection rate, false positive rate and the mean and (intra- and interparticipant) standard deviation of the timing error for Heel Strikes and Toe-Offs. We show that position-based algorithms give well-balanced results and are able to outperform the acceleration-based algorithms in all five metrics. Additionally, we propose and compare several methods for detecting left and right steps, thereby enabling quantification of the full gait cycle.
...
Gait event detection allows for insight into one’s gait pattern, an invaluable aid in rehabilitation. Current methods often rely on measured acceleration and rarely on position measurements [3]–[6]. In this paper we propose 4 novel gait detection methods based on the position of the Center of Mass (one approach being causal and thus suitable for real-time use) and compare them to 4 existing state-of-the-art acceleration- based methods. All algorithms are benchmarked on an existing data set (overground walking, 23 participants, 1772 steps), comparing the detection rate, false positive rate and the mean and (intra- and interparticipant) standard deviation of the timing error for Heel Strikes and Toe-Offs. We show that position-based algorithms give well-balanced results and are able to outperform the acceleration-based algorithms in all five metrics. Additionally, we propose and compare several methods for detecting left and right steps, thereby enabling quantification of the full gait cycle.