arXiv subjects

Faraz Ashtiani

Publications and source records attributed to Faraz Ashtiani.

3 recordsLinked to original sources

arXiv2021

Optimal Pacing of a Cyclist in a Time Trial Based on Individualized Models of Fatigue and Recovery

This paper formulates optimal pacing of a cyclist on hilly terrain time-trials as a minimum-time optimal control problem. Maximal power of a cyclist serves as a time-varying constraint and depends on fatigue and recovery which are captured via dynamic models proposed early in the paper. Experimental protocols for identifying the individualized parameters of the proposed fatigue and recovery models are detailed and results for six human subjects are shown. In an analytical treatment via necessary conditions of Pontryagin Minimum Principle, we show that the cyclist's optimal power in a time-trial is limited to only four modes of all-out, coasting, pedaling at a critical power, or constant speed (bang-singular-bang). To determine when to switch between these modes, we resort to numerical solution via dynamic programming. One of the subjects is then simulated on four courses including the 2019 Duathlon National Championship in Greenville, SC. The dynamic programming simulation results show 24% reduction in travel time over experimental results of the self-paced subject who is a competitive amateur cyclist. The paper concludes with description of a pilot lab experiment in which the subject trial time was reduced by 3% when the near-optimal pace was communicated to her in real-time.

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arXiv2020

Multi-Intersection Traffic Management for Autonomous Vehicles via Distributed Mixed Integer Linear Programming

This paper extends our previous work in [1],[2], on optimal scheduling of autonomous vehicle arrivals at intersections, from one to a grid of intersections. A scalable distributed Mixed Integer Linear Program (MILP) is devised that solves the scheduling problem for a grid of intersections. A computational control node is allocated to each intersection and regularly receives position and velocity information from subscribed vehicles. Each node assigns an intersection access time to every subscribed vehicle by solving a local MILP. Neighboring intersections will coordinate with each other in real-time by sharing their solutions for vehicles' access times with each other. Our proposed approach is applied to a grid of nine intersections and its positive impact on traffic flow and vehicles' fuel economy is demonstrated in comparison to conventional intersection control scenarios.

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arXiv2020

Experimental Modeling of Cyclists Fatigue and Recovery Dynamics Enabling Optimal Pacing in a Time Trial

Improving a cyclist performance during a time-trial effort has been a challenge for sport scientists for several decades. There has been a lot of work on understanding the physiological concepts behind it. The concepts of Critical Power (CP) and Anaerobic Work Capacity (AWC) have been discussed often in recent cycling performance related articles. CP is a power that can be maintained by a cyclist for a long time; meaning pedaling at or below this limit, theoretically, can be continued for infinite amount of time. However, there is a limited source of energy for generating power above CP. This limited energy source is AWC. After burning energy from this tank, a cyclist can recover some by pedaling below CP. In this paper we utilize the concepts of CP and AWC to mathematically model muscle fatigue and recovery of a cyclist. Then, the models are used to formulate an optimal control problem for a time trial effort on a 10.3 km course located in Greenville SC. The course is simulated in a laboratory environment using a CompuTrainer. At the end, the optimal simulation results are compared to the performance of one subject on CompuTrainer.

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