Related papers: On minimizing cyclists' ascent times: Part II
We prove that, given an average power, the ascent time is minimized if a cyclist maintains a constant ground speed regardless of the slope. Herein, minimizing the time is equivalent to maximizing -- for a given uphill -- the corresponding…
Many time-trial and triathlon bicycle races take place on relatively flat, closed-circuit courses. In the absence of hills, riding-speed is limited almost solely by aerodynamic drag; consequently, winds can have a big effect on elapsed…
We present a mathematical model for optimizing breakaway strategies in competitive cycling, balancing power expenditure, aerodynamic drag, and crashing. Our framework incorporates probabilistic crash dynamics, allowing a cyclist's risk…
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…
VAM ({\it velocit\`a ascensionale media}) is a measurement that quantifies a cyclist's climbing ability. We show that to minimize the time to attain a given height gain\, -- \,which is tantamount to maximizing VAM\, -- \,a cyclist should…
With the advent of power-meters allowing cyclists to precisely track their power outputs throughout the duration of a race, devising optimal power output strategies for races has become increasingly important in competitive cycling. To do…
We propose a novel method for planning shortest length piecewise-linear motions through complex environments punctured with static, moving, or even morphing obstacles. Using a moment optimization approach, we formulate a hierarchy of…
We investigate the dynamics of a bicycle on an uneven mountain bike track split into straight sections with small jumps (kickers) and banked corners. A basic bike-rider model is proposed and used to derive equations of motion, which capture…
We combine power-meter measurements with GPS measurements to study the model that accounts for the use of power by a cyclist. The model takes into account the change in elevation and speed along with adverse effects of air, rolling and…
Trajectory optimization for autonomous vehicles usually relies on the kinematic bicycle model because of its computational simplicity. However, when the planned trajectory is executed under the true vehicle dynamics, which include lateral…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
We formulate a phenomenological model to study the power applied by a cyclist on a velodrome\, -- \,for individual timetrials\, -- \,taking into account the straights, circular arcs, connecting transition curves and banking. The dissipative…
Predicting cycling duration for a given route is essential for training planning and event preparation. Existing solutions rely on physics-based models that require extensive parameterization, including aerodynamic drag coefficients and…
This paper proposes a two-stage approach to formulate the time-optimal point-to-point motion planning problem, involving a first stage with a fixed time grid and a second stage with a variable time grid. The proposed approach brings…
Cyclic coordinate descent is a classic optimization method that has witnessed a resurgence of interest in machine learning. Reasons for this include its simplicity, speed and stability, as well as its competitive performance on $\ell_1$…
Understanding the criteria that bicyclists apply when they choose their routes is crucial for planning new bicycle paths or recommending routes to bicyclists. This is becoming more and more important as city councils are becoming…
This paper presents for the first time an approach to minimize direct operational costs (DOC) for all-electric aircraft during the climb phase, introducing a time-varying cost index (CI). The CI is modeled as a dynamic parameter commanded…
We develop a convergence-rate analysis of momentum with cyclical step-sizes. We show that under some assumption on the spectral gap of Hessians in machine learning, cyclical step-sizes are provably faster than constant step-sizes. More…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
In this article, we are interested in optimal aircraft trajectories in climbing phase. We consider the cost index criterion which is a convex combination of the time-to-climb and the fuel consumption. We assume that the thrust is constant…