正交Padé激活函数可训练激活函数，用于在深度网络中平滑和快速收敛

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正交Padé激活函数可训练激活函数，用于在深度网络中平滑和快速收敛_Orthogonal-Padé Activation Functions Trainable Activation functions for smooth and faster convergence in deep networks.pdf 【正交Padé激活函数】是深度学习领域中一种创新的可训练激活函数，它旨在提升神经网络模型的平滑性和收敛速度。正交Padé激活函数基于数学中的Padé近似理论，这是一种高阶多项式逼近方法，常用于解析延拓和数值积分。在深度学习中，激活函数的作用是引入非线性，使网络能够处理更复杂的模式和关系。传统的激活函数如ReLU、Sigmoid和Tanh虽然有效，但可能会遇到梯度消失或梯度爆炸的问题，影响网络的训练效率。正交Padé激活函数通过构造一组正交多项式对，使得在某些特定点上能够精确地近似目标函数，这有助于减少训练过程中的波动和不稳定性，从而实现更快的收敛。此外，由于其内在的性质，这种激活函数可以提供更好的局部线性化，使得网络的优化过程更加平滑，减少了训练过程中可能遇到的局部最小值问题。在实际应用中，正交Padé激活函数可以通过微调其参数来适应不同的任务和数据集，增强了模型的泛化能力。这种可训练性使得激活函数可以针对特定问题进行优化，而不仅仅是使用固定的函数形式。在深度网络中使用这种激活函数，有可能显著提高模型的性能，特别是在大型和复杂的网络结构中，其优势可能更为明显。【自动驾驶自行车共享系统】则是城市可持续交通解决方案的一个实例，它融合了车辆共享、电动化、自主驾驶以及微观移动性的优点。随着全球人口增长和气候变化等挑战，重新思考城市设计和移动方式变得至关重要。自行车共享系统可以有效地减少交通拥堵，提高城市生态效率，而自动驾驶技术的引入则有望进一步提升系统的效率和用户体验。论文中提出的【自适应代理模拟器】是评估这种系统性能的关键工具。它能模拟真实场景下自动驾驶自行车共享系统的车队行为，并基于需求预测实现自动再平衡。通过调整不同参数，研究者量化了自主系统如何改善效率和服务质量，并发现即使没有再平衡机制，自动驾驶自行车共享系统也能以比传统车站式或无桩式系统更小的车队规模提供更好的性能和体验。这表明，尽管自动驾驶自行车的成本较高，但其显著的效率优势可能足以抵消这部分增加的成本。关键词：正交Padé激活函数、深度学习、人工智能、计算机科学、自动驾驶、自行车共享系统、模拟器、效率、服务质量和用户体验。

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Simulation study on the ﬂeet performance of shared autonomous bicycles

Naroa Coretti Sanchez

a,1,∗

, I˜nigo Martinez

b,1

, Luis Alonso Pastor

, Kent Larson

MIT Media Lab, Cambridge, MA, USA

University of Navarra, San Sebastian, Spain

Abstract

Rethinking cities is now more imperative than ever, as society faces global challenges such as population

growth and climate change. The design of cities can not be abstracted from the design of its mobility

system, and, therefore, eﬃcient solutions must be found to transport people and goods throughout the city

in an ecological way. An autonomous bicycle-sharing system would combine the most relevant beneﬁts of

vehicle sharing, electriﬁcation, autonomy, and micro-mobility, increasing the eﬃciency and convenience of

bicycle-sharing systems and incentivizing more people to bike and enjoy their cities in an environmentally

friendly way. Due to the uniqueness and radical novelty of introducing autonomous driving technology

into bicycle-sharing systems and the inherent complexity of these systems, there is a need to quantify the

potential impact of autonomy on ﬂeet performance and user experience. This paper presents an ad-hoc agent-

based simulator that provides an in-depth understanding of the ﬂeet behavior of autonomous bicycle-sharing

systems in realistic scenarios, including a rebalancing system based on demand prediction. In addition, this

work describes the impact of diﬀerent parameters on system eﬃciency and service quality and quantiﬁes the

extent to which an autonomous system would outperform current bicycle-sharing schemes. The obtained

results show that with a ﬂeet size three and a half times smaller than a station-based system and eight

times smaller than a dockless system, an autonomous system can provide overall improved performance

and user experience even with no rebalancing. These ﬁndings indicate that the remarkable eﬃciency of an

autonomous bicycle-sharing system could compensate for the additional cost of autonomous bicycles.

Keywords: future mobility; bicycle-sharing systems; autonomous vehicles; micro-mobility; agent-based

simulation; multi-agent systems;

1. Introduction

The global population is projected to grow to 9.7 billion by 2050 [1]. Combined with the eﬀect of

urbanization, this process could add 2.5 billion people to urban areas [2]. In 2018, 55% of the world’s

population lived in cities, and this number is expected to grow to 68% by 2050 [2]. Population growth poses

a challenge for sustainable development [1], making the need for rethinking cities each time more imperative.

Challenges such as climate change, along with other issues such as social inequality or the recent COVID-19

pandemic, are constantly reminding us of the urgency of designing cities to be more sustainable, equitable,

and resilient.

The design of cities cannot be abstracted from the design of their transport systems [3]; therefore, when

considering the future of cities, the transportation of people and goods throughout the city becomes a key

challenge. At the MIT Media Lab City Science group, we envision future cities to have a human scale,

composed of dense and diverse districts where all the resources and amenities needed in daily life can be

∗

Corresponding author

Email addresses: naroa@mit.edu (Naroa Coretti Sanchez ), imartinezl@alumni.tecnun.es (I˜nigo Martinez ),

alonsolp@mit.edu (Luis Alonso Pastor), kll@mit.edu (Kent Larson)

These authors contributed equally to this work.

arXiv:2106.09694v2 [cs.CY] 21 Jun 2021

found within a walkable distance [4]. In these districts, most of the trips would be one-person, short distance,

and low speed, reducing car dependency and favoring walking and sustainable micro-mobility systems [4–6].

In this scenario, micro-mobility systems could be a solution for these short-distance trips and provide the

ﬁrst- and last-mile connection to mass transit. Furthermore, micro-mobility solutions could also be used for

package or food delivery when not in use by riders [6].

With this image of a future city in mind, the MIT Media Lab City Science research group has developed

several mobility solutions over the last decades. These solutions include vehicles such as the CityCar

lightweight electric folding automobile, or the PEV, an autonomous three-wheeler designed for shared use

[7, 8]. One of the most recent projects is the MIT Autonomous Bicycle Project: a novel system that

aims to bring autonomy into bicycle-sharing systems (BSS) [9]. Autonomous driving capabilities would

transform BSS into an on-demand mobility system, radically increasing the convenience of bike-share [9].

In an autonomous BSS, a user would be able to request a trip through a mobile app, and an autonomous

bicycle would drive to the user’s location. Then, the user would ride the autonomous bicycle just like a

regular bicycle. Upon arrival to the destination, the bicycle would drive autonomously to pick up another

user, to a charging station, or towards wherever the demand is predicted to occur.

We envision this bike to be part of the ecosystem of shared and autonomous micro-mobility in future

walkable cities, as well as a new approach to current bicycle-sharing systems. Governments all over the

world have been promoting public BSS, intending to improve mobility and public health and introduce

a sustainable mode of transportation [10]. Especially in the last 15 years, BSS have quickly proliferated,

increasing from 17 station-based systems worldwide in 2005 to over 2000 in 2019 [9].

However, current BSS still face several challenges, among which it is worth highlighting the rebalancing

problem caused by uneven travel patterns and the oversupply of bicycles that often happens in dockless

systems [11–15]. Autonomous bicycles could be the solution to these challenges: For the system operators,

it would solve the rebalancing problem and make the sharing system more eﬃcient, with higher vehicle

utilization rates and smaller ﬂeet sizes. Moreover, having bicycles with autonomous driving capabilities

would bring the convenience of mobility-on-demand into the current BSS, improving user experience. This

article aims to describe and quantify to which extent an autonomous system would outperform the current

BSS.

Most of the previous research around the performance of shared autonomous vehicles has been focused

on cars or taxis. Narayanan et al. [16] provide an overview of the relevant studies in the ﬁeld of shared

autonomous vehicle (SAV) services published from 1950 to 2019. This overview covers the most relevant

work done in terms of simulations SAV [17–25] and provides a comparison of the main results. While this

overview explicitly warns that bike-sharing and scooter-sharing systems are not considered in the study,

there are several similarities between simulations of other shared autonomous vehicles, such as cars, taxis,

or buses, and shared autonomous bikes. Therefore, we recommend visiting the overview mentioned above

for further details. With regards to simulations related to autonomous micro-mobility, Grignard et al.

[26] proposed a generic simulation framework that allows for modeling diﬀerent future mobility modes and

understanding their impact on traﬃc and congestion. Recently, Kondor et al. [27] presented a simulation

study of the impact of a ﬂeet of autonomous scooters.

Due to the uniqueness and radical novelty of introducing autonomous driving technology into BSS

and the inherent complexity of these systems, there is the need to quantify the potential impact that

autonomy might have on the ﬂeet performance and user experience. Consequently, this paper presents an

ad-hoc simulator that provides an in-depth understanding of the ﬂeet behavior of an autonomous BSS, how

diﬀerent parameters aﬀect the performance, and a quantiﬁcation of the extent to which it outperforms the

current BSS. These simulations were conducted considering the most realistic possible scenarios, including

a rebalancing system based on demand prediction.

The remainder of the paper is organized as follows. Section 2 describes some central aspects for the

mobility modes of future walkable cities. Section 3 analyzes how autonomous bicycles can pose a new

and more eﬃcient approach to BSS. Then, Section 4 describes the architecture of the proposed agent-based,

discrete event simulation framework along with its main features. The three BSS under study are also deﬁned

and formalized in this section. Section 6 gathers the results of the simulation for the autonomous system and

current station-based and dockless systems, comparing their performance under diﬀerent scenarios. This

section also quantiﬁes the performance of a rebalancing system based on demand prediction and analyzes

how the diﬀerent conﬁguration parameters impact the performance metrics. Finally, Section 7 concludes by

highlighting the main conclusions of this study and providing an outline for future work.

2. Mobility in future walkable cities: the power of combining transformative ideas

Cities are in need of a change in the approach to urban design. The vision of the City Science group is that

humans, and not cars, should be at the center of how we design cities, promoting sustainable transportation

modes such as walking and the use of micro-mobility systems. These human-scale cities would be composed

of a network of walkable districts that have mixed land uses and oﬀer places to live and work to a diverse

group of people. In addition, the amenities needed to cover people’s needs in their daily lives (e.g., cafeterias,

schools, hospitals, grocery stores) will also be included in these districts, drastically reducing the need for

commuting.

In this scenario, most of the trips would be one person, short distance, and low speed. As a consequence,

walking or micro-mobility systems could be a solution for these short-distance trips, as well as providing the

ﬁrst- and last-mile connection to mass transit when traveling between districts [4–6]. These micro-mobility

systems should be adequately designed to create an ecological, eﬃcient, and equitable urban transportation

network that solves current urban challenges. We believe that to achieve these goals, vehicle sharing,

electriﬁcation, autonomy, and micro-mobility have to be wisely combined in a way that increases their

potential.

Vehicle sharing combines the eﬃciency of public transportation with the convenience of privately owned

vehicles[28] and, according to various studies, can lead to a very signiﬁcant reduction in the number of

vehicles [19, 29, 30]. Moreover, as the cost of ownership is shared, it can promote the use of electric vehicles,

which have a high purchasing cost but low operating costs [28].

Electriﬁcation has been at the center of the innovation eﬀorts of automotive companies for many years

already [31]. Some studies highlight that electric vehicles show lower life-cycle greenhouse gas emissions than

conventional internal-combustion-engine vehicles, both for the vehicle and fuel [32], which is very relevant

considering that, for example, in 2018, the transportation sector accounted for the 28.3% of the greenhouse

gas emissions in the US [33]. It must be noted that other authors warn that there are some other indicators,

such as human toxicity and terrestrial acidiﬁcation, that are worsened and should be taken into consideration

in the vehicle electriﬁcation process [34]. However, as the overall beneﬁt of electriﬁcation depends on the

energy mix of the country, there is a clear potential for greater beneﬁts if we think of a future where most of

the energy will be generated by renewable energy [34]. Another remarkable beneﬁt of electric vehicles is the

possibility of using the batteries of the electric vehicles to improve the performance of the electric grid. The

energy storage capacity in vehicles could be used to compensate for the irregular supply of some renewable

energy sources such as photo-voltaic panels in cloudy weather, as well as to balance the supply and demand

of the electric grid [35].

With regards to autonomous driving technology, there is some evidence that privately-owned autonomous

vehicles could increase the number of vehicles in the streets due to the reduction in the value of travel time

losses [36] and the increase in the segment of the population that can drive [37]. Autonomous vehicles

could also introduce extra empty trips to, for example, pick up a delivery. Nevertheless, facts change when

considering autonomy in shared ﬂeets. According to Cervero [38], the combination of autonomy and car-

sharing could be the next paradigm shift for mobility in the US. While there might still be a slight increase

in vehicle kilometers traveled (v.k.t.) due to rebalancing and induced demand, increased eﬃciency would

lead to reduced emissions, increased vehicle utilization rates, and consequently smaller ﬂeet sizes [16]. The

convenience of vehicle sharing systems could also be increased by the introduction of autonomous vehicles

thanks to the vehicles being able to drive to wherever the demand is emerging, instead of the user having to

ﬁnd the vehicle [24]. Finally, autonomous vehicles could serve areas that are not well connected by public

transportation, working as a ﬁrst or last-mile solution and improving access to mass transit [39].

While the term ’autonomous vehicles’ generally refers to cars, working with smaller and more lightweight

vehicles can present numerous advantages. In the US, the number of micro-mobility trips increased from

35 million in 2017 to 84 million in 2018 and 136 million in 2019 [40]. Lighter vehicles consume less energy

[41], at lower speeds, the computational demand is decreased, and collisions at lower speeds and lighter

vehicles are less deadly [42, 43]. Hence, from the point of view of regulation, it is likely that autonomous

micro-mobility solutions may be deployed at a large scale in cities sooner than autonomous cars.

Vehicle sharing, electriﬁcation, autonomy, and micro-mobility sharing can have the greatest impact if

combined. According to Greenblatt et al. [44], by 2030, each autonomous taxi implemented could reduce the

GHG emission per mile traveled in the US 87-94% below internal combustion engine vehicles, as a result of

sustainable power generation, ﬂeet size reduction, and more cost-eﬀective high-performance electric vehicles.

We believe that translating these characteristics into micro-mobility systems could lead to the ideal mobility

solution for future walkable cities.

In light of the above, it can be concluded that, while some of the above concepts have previously been

explored, if combined in a new way, they can lead to solutions that transform urban mobility, making cities

more livable, equitable, and sustainable.

3. Autonomous bicycles as a new generation of bicycle-sharing systems

3.1. Insight into current bicycle-sharing systems

In recent years, BSS have become a mainstream solution for inner-city transportation in countries such

as the US [40] with the goal of introducing a sustainable mobility mode that can help to alleviate urban

congestion problems [10]. As a result, the number of station-based BSS grew from 17 systems in 2005 to

2147 in 2019 worldwide (Figure 1).

Figure 1: Evolution of the number of station-based bicycle-sharing schemes worldwide [9].

The ﬁrst BSS are dated as early as 1965, but it took several generations of introducing new technologies,

mainly to avoid theft and vandalism before BSS became successful [45]. BSS typically provide a short-term

rental of bicycles that can be picked up and returned in diﬀerent locations. Currently, there are two main

types of BSS: station-based systems and dockless systems. Station-based systems have a number of stations

with several docking racks where users can either pick up or return bicycles [46]. In this system, the bicycles

can only be picked up from or returned at stations, limiting the use of BSS to the area where stations are

available. More recently, GPS enabled a new way of bike-sharing which is called dockless bike-sharing [11].

In this case, users can ﬁnd available bicycles via a mobile app, and bikes can be dropped oﬀ at any location

within the service region [46].

However, despite the improvements made throughout the various generations of BSS and its current

popularity, some challenges must be faced in terms of eﬃciency, sustainability, and user experience. The

remainder of this section describes two main challenges that are system rebalancing and bicycle oversupply.

System rebalancing has been stated to be one of the biggest challenges of BSS by numerous studies: H Si

et al. [11] claim that the imbalance of the systems is the most urgent problem since the implementation of

third-generation bicycle shares. Curran [12] refers to successful bicycle redistribution as one of the critical

success factors in bicycle sharing schemes. Additionally, other sources such as Shaheen and Guzman [47]

also highlight that the problem of ﬁnding available bikes and docks is one of the main complaints from users.

The content and evolution of the research in recent years also showcase the importance of the rebalancing

problem. In a scientometric literature review, Hongyun Si et al. [11] found that seven out of the ten most

co-cited articles on bike-sharing systems between 2010 and 2018 referred to large-scale systems, demand

prediction, and rebalancing problems.

The rebalancing problem occurs as a consequence of the spatial and temporal imbalance in commuting

patterns and topographic landmarks like hills because users travel more often downhill than uphill [48]. In

station-based systems, each station has a limited capacity, and the rebalancing problem leads to stations

frequently lacking bicycles or docks [49]. In dockless systems, even if there is not a capacity restriction

related to stations, ﬁnding available bicycles remains a problem due to trip ﬂow imbalance [50].

These experiences increase travel times and are detrimental to the user experience. Some studies found

that not being able to ﬁnd available bicycles and docks was the most frequent complaint among users [51],

which led to frustration and loss of reliability in the system [48, 52]. This loss of reliability is particularly

important since unreliability results in a negative eﬀect in mode choice for commute trips, even for those

who have ﬂexible work schedules [53]. This issue generates distrust in the system and could eventually lead

to shifting to another mode of transportation.

Operators use vans and trucks to transport bicycles from saturated areas and mitigate the impact of

the rebalancing problem. However, this process has a very high economic and ecological cost; redistribution

is both the main contributor to the operational cost of bicycle-sharing schemes [54] and also the primary

source of GHG emissions in the life-cycle of both station-based and dockless systems [46].

Bicycle oversupply in dockless systems has been another source of great concern. Dockless systems

quickly proliferated around 2016 in China, the country with the largest dockless bike-sharing market [55].

Dockless bike-sharing was introduced in China in late 2015 [56], and from 2016 to 2017, the ﬂeet of dockless

systems grew from 2 million to 23 million [55].

Not being restricted by the number of docks, dockless systems can be up to 10 to 60 times larger than

the existing station-based systems [55]. These ﬂeet sizes vastly exceed the infrastructure capacities of cities,

provoking urban problems such as the presence of dockless bicycles parked illegally clogging sidewalks [57].

The number of bicycles also exceeds user demand, causing low levels of use of the bicycles and system

ineﬃciency [11].

As a consequence of these problems, dockless systems are currently facing a backlash from cities. Some

cities have started to limit the number of bikes, while others have forced operators to cease their programs

[15, 55]. In China, from 2017 to 2019, the growth rate of dockless bike-sharing decreased from 631.2% to

10.3% [57]. The saturation of the market has caused many companies to go bankrupt, and the amount of

discarded bicycles has generated an enormous recycling crisis [57].

Overall, the severity of the problems faced with current BSS shows a need for disruptive innovation for

bicycle-sharing to be the eﬃcient, convenient, economical that our cities need.

3.2. The MIT Autonomous Bicycle Project

The MIT Media Lab City Science Group proposes MIT Autonomous Bicycle as a mobility solution

for future walkable cities (Figure 2). As an alternative for short-distance trips and providing an eﬃcient

connection to mass transit, they could encourage more people to bike and make trips in environmentally

friendly ways. At the same time, autonomous bicycles could serve as an alternative to the current BSS,

providing a convenience that has not been achieved with other systems.

Using this new system, whenever a user requested a ride, a bicycle would drive autonomously to pick

up the user. Then, the user would ride it just as a regular bicycle and, upon arrival to the destination, the

bicycle would go back to autonomous mode to drive for the next user or ﬁnd a charging station.

Compared to other autonomous vehicles, bicycles have the additional challenge of lack of lateral stability.

As bicycles have just two wheels, bicycles tend to tip over to the side without additional support. We

have tackled this issue by designing a novel system that allows the bicycle to transform into a tricycle for

autonomous driving.

When a user is riding it, the system is in bicycle mode. In this conﬁguration, the two rear wheels act

as a single wheel, and the riding experience remains unchanged from riding a regular bike (Figure 3a). In

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正交Padé激活函数可训练激活函数，用于在深度网络中平滑和快速收敛_Orthogonal-Padé Activation Fun

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