自主车辆感知与控制：陆地、海洋和空中的应用

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"Sensing and Control for Autonomous Vehicles: Applications to Land, Water and Air" 该书是一部由Thor I. Fossen、Kristin Y. Pettersen和Henk Nijmeijer编辑的关于自动驾驶车辆感测与控制技术的精选文集。书中重点关注了陆地、水上和空中自主车辆的导引、导航和运动控制系统。随着技术的发展，这些系统在各种操作中的重要性日益增加。例如，自主水下车辆(AUVs)用于管道检查、轻度干预工作、水下调查和海洋学/生物学数据收集，而自主无人驾驶航空系统(UAVs)则广泛应用于检测、监控、数据收集和监视等领域。当前，尽管已有一定程度的自主性，但大多数车辆仍处于有限的智能操作阶段。因此，对于合作协调的多车辆系统、实时重新规划、稳健的自主导航系统以及车辆的稳健自主控制的研究兴趣正在增长。高度自主的无人车辆有望实现安全高效的数据采集，促进气候和环境模型的同化，并补充全球卫星系统。本书的目标读者主要是控制理论领域的研究专家，但也适合对此感兴趣的研究生学习。通过这本书，读者可以深入了解自动驾驶车辆在不同环境下的应用，包括关键的传感器技术、导航算法、动态控制策略以及针对不确定性和环境变化的鲁棒性设计。书中的内容可能涵盖以下知识点： 1. **自动驾驶的基础**：介绍自动驾驶的基本原理，包括车辆定位、路径规划、决策制定和行为控制等。 2. **传感器技术**：详述各种传感器（如激光雷达、摄像头、惯性测量单元和GPS）在感知环境、避障和定位中的作用。 3. **导航系统**：讨论全球导航卫星系统、惯性导航系统和其他辅助导航技术，以及它们如何提供精确的位置信息。 4. **运动控制**：介绍如何设计和实施控制策略来确保自主车辆的稳定行驶和精确机动。 5. **多车辆协作**：探讨多个自主车辆如何协同工作以完成复杂的任务，例如编队飞行或搜索与救援任务。 6. **实时重新规划**：讲解在动态环境中如何快速调整路径和任务规划。 7. **鲁棒自主导航**：研究如何在不确定性、传感器故障或通信限制条件下设计稳健的自主导航系统。 8. **环境数据收集**：介绍如何利用自主车辆进行环境监测，例如大气污染检测、海洋生态系统研究等。 9. **安全性和可靠性**：分析自动驾驶车辆的安全挑战和保证其可靠性的方法。 10. **未来趋势**：讨论自动驾驶技术的最新发展和未来可能的方向，如全自动化交通系统和智能城市应用。通过深入阅读本书，读者将能够获得对自动驾驶车辆技术的全面理解，从而为研究和开发更高级别的自主系统提供理论基础和技术支持。

Observers for Position Estimation Using Bearing and Biased Velocity Information 7

Deﬁnition 2 A direction y(t) ∈ S

n−1

, is called persistently exciting if there exist

δ>0 and 0 <μ<δsuch that for all t



t+δ

y(τ )

dτ ≥ μI, with π

= (I −yy



) (3)

For future use, note that (3) is equivalent to

For all b ∈ S

n−1

then



t+δ

|π

y(τ )

dτ ≥ μ, (4)

Another characterization of persistence of excitation, in terms of the property that

the time-derivative of ˙y must satisfy, is provided in the following lemma.

Lemma 1 Assume that ˙y(t) is uniformly continuous, then relation (3) (respectively

(4)) is equivalent to:

There exists (δ, ε) > 0 and τ ∈[t, t +δ] such that |˙y(τ )|≥ε (5)

Proof The proof of this lemma is given in Appendix.

Lemma 2 The system (1)–(2), complemented with the equation ˙a = 0, with X =









as the system state vector, v as the system input, and a single direction y

as the system output, is weakly observable but not strongly observable.

Proof Choose, for instance, the input v(t) = (cos(t), sin(t), 0 ...0)

. The solutions

to the system are then given by x(t) = x(0) + (sin(t) + at, −cos(t) + at, 0 ...0)

and one easily veriﬁes that y

(t) = y

(t), ∀t, implies that x

(0) = x

(0). This estab-

lishes the weak observability property of the system. Note also that the chosen input

renders both outputs y

(t) and y

(t) persistently exciting in the sense of the deﬁnition

(2). On the other hand, one veriﬁes that, if the input v is constant, then initial states

(0) = k

v and x

(0) = k

v, with k

and k

denoting arbitrary positive numbers,

cannot be distinguished because y

and y

are constant and equal in this case. This

proves that the system is not strongly observable.

The weak observability property of the system justiﬁes the introduction of the per-

sistence condition (3) to characterize “good” outputs (produced by “good” inputs)

yielding a property of “uniform” observability that renders the state-observation

problem (addressed in the next section) well posed.

For the case for more than 1 known target-points location, the criterion of strong

observability is given by items 1 and 2 of the following lemma.

Lemma 3 Let deﬁne Q :=



l−1

i=0

(t)

. Then the persistency of excitation (Deﬁni-

tion 2):



t+δ

Q(τ )dτ ≥ μI,

Observers for Position Estimation Using Bearing and Biased Velocity Information 9

and hence one can verify that a linear observer of the form:

ˆx = v + K

−ˆx) = v + K

˜x, with K

∈ M

, (6)

ensures the global exponential convergence of the error ˜x to zero.

The main drawback of this observer is that it is not well deﬁned at times when

Q(t) is singular and that it is ill conditioned when Q(t) tends to become singular

corresponding, for instance, to the weak observability case. A solution to this problem

consists in choosing K

= K

(t) such that the problematic term Q(t)

−1

(or the direct

measure x

of x) is not needed anymore. To this aim, it sufﬁces to set K

= KQ(t),

with K ∈ M

The following lemma summarizes the effect of the above choice of K

leading

to an observer that encompasses the strong and weak observability cases with any

number of target-points with known location.

Lemma 4 Consider the system (1)–(2) and redeﬁne observer (6) with K

= KQ(t)

as follows:

ˆx = v − K

l−1



i=0

(t)

(ˆx − p

), ˆx(0) =ˆx

∈ R

and K ∈ M

(7)

Assume that a ≡ 0, x is bounded and x − p

never crosses zero, so that the output y

(t)

is always well deﬁned for i = 0,...,l − 1. Assume that the persistence condition

on Q(t), Lemma3, is satisﬁed. Then the estimation error ˜x = x −ˆx = 0 is uniformly

globally exponentially stable (UGES).

Proof Using the fact that π

(t)

(x − p

) = 0, ∀i = 1,...,l − 1, on can remark that

ˆx = v − KQ(t)˜x,

and hence

˜x =−KQ(t)˜x. Deﬁning w = K

−

˜x and using the above dynamics of ˜x

one gets the following linear time-varying system:

˙w =−K

Q(t)K

w, (8)

Using the assumption of persistent excitation characterized by relation (3) a direct

application of [21, Lemma 5] proves that ˜x is UGES. More explicitly, one veriﬁes

that the transition matrix Φ

associated with the above system ( 8) satisﬁes

||Φ

(t,τ)|| ≤ exp

−γ(t−τ)

, (9)

where γ = μk



δ(1 + lk

δ)



and k

represent respectively the lowest

and the largest eigenvalues of K.

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