视觉控制与通用方法：轮式移动机器人

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“Visual Control of Wheeled Mobile Robots”是SpringerTracts in Advanced Robotics系列的第103卷，由Héctor M. Becerra和Carlos Sagüés合著。本书探讨了轮式移动机器人（WMRs）的视觉控制，特别强调了在通用方法中统一视觉与控制的理论与实践。在机器人技术领域，视觉控制是一种关键的技术，它允许机器人通过摄像头或其他视觉传感器获取环境信息，然后处理这些信息以指导其运动和行为。对于轮式移动机器人，这种技术尤为重要，因为它们需要在不断变化的环境中导航，避开障碍物，并执行复杂的任务。本书深入研究了如何将机器视觉与控制理论相结合，以实现更高效、准确的机器人操作。机器视觉是这个领域的核心部分，它涵盖了图像处理、特征识别、目标检测和跟踪等多个子领域。在WMRs中，视觉系统可以帮助机器人理解周围环境，创建地图，进行定位（例如，通过SLAM，即同时定位与建图），并做出决策以规划最优路径。此外，视觉系统还可以用于识别特定物体或标志，这对于诸如物品搬运或服务机器人等应用至关重要。控制理论则涉及到如何设计算法使机器人按照预期的方式运动。这包括经典控制理论，如PID控制器，以及现代控制理论，如模型预测控制和最优控制。在视觉控制的背景下，控制策略需要能够快速响应视觉传感器提供的实时数据，并适应环境的变化。作者Héctor M. Becerra和Carlos Sagüés在书中详细阐述了这些概念，并可能提供了具体的案例研究和实验结果，以展示理论如何应用于实际的WMR系统。他们可能还讨论了如何克服视觉控制中的挑战，如光照变化、图像噪声、计算复杂性以及实时性要求。编辑Bruno Siciliano和Oussama Khatib是机器人学界的知名专家，他们的贡献确保了该书的学术水平和专业性。编辑顾问委员会由来自全球各地的顶尖学者组成，他们在机器人学的各个分支都有深厚的造诣，这进一步保证了本书内容的广泛性和深度。 “Visual Control of Wheeled Mobile Robots”是关于如何利用机器视觉和控制理论提升WMR性能的一部重要著作，对研究人员、工程师和学生来说都是一份宝贵的参考资料。通过阅读这本书，读者可以深入了解视觉感知和控制融合在机器人系统设计中的最新进展和未来趋势。

1.2 State of the Art on Visual Control 5

moving object by tracking it and estimating its velocity is presented in [33]. A con-

trol theoretic formulation (linear time-invariant LTI) and a controller design method

(linear quadratic LQ) for an image-based visual servoing with redundant features is

proposed in [61]. In [44], motion in the image is used as input to the control system.

This motion can be estimated without any a priori knowledge of the observed scene

and thus, it does not need visual marks on the observed scene to retrieve geometric

features. Some efforts have been developed to deal with the dependence on depth of

the features in the classical image-based visual servoing. On this issue, an extended

2D visual servoing that augments the task function with an estimated depth distri-

bution of the target points and an estimated camera model to avoid local minima is

developed in [125]. Another approach dealing with the estimation of feature depth

for image-based visual servoing using a nonlinear observer is presented in [90]. The

image-based visual servoing schemes are sensitive to noise and often, they require

to apply some ﬁltering technique for smoothing the visual measurements. Lines and

moments have been proposed to achieve robustness to image noise. Additionally,

lines facilitate detection [7], and image moments remove potential problems with

redundant points [30]. Image-based visual servoing has achieved good decoupling

and linearizing properties for 6 degrees of freedom using image moments [131].

The image-based visual servoing approach has concerned about some important

issues in order to overcome the drawbacks of the approach, for instance, to keep

the features in the ﬁeld of view or to avoid local minima [36]. In [128], the ability

of a computer vision system to perceive the motion of an object in its ﬁeld of view

is addressed. A quantitative measure of motion is derived and called perceptibility,

which relates the magnitude of the rate of change in an object’s position to the

magnitude of the rate of change in the image of that object. This has derived to path

planning strategies for image-based visual servoing. In [98], the robot redundancy

for dynamic sensor planning is used for visual servoing through the minimization of

a secondary cost function. A partitioned approach for image-based visual servoing

that overcomes the problem that the robot executes desired trajectories in the image,

but which can be indirect and seemingly contorted in Cartesian space is introduced

in [40]. A potential function that repels feature points from the boundary of the

image plane is incorporated to guarantee that all features remain in the image. In

[107], planning in image space and image-based visual servoing are coupled to solve

the difﬁculties when the initial and desired robot positions are distant. The proposed

method is based on the potential ﬁeld approach. The work in [37] deals with the

problem of visual servoing for robot manipulators taking into account constraints

such as visibility, workspace and joint constraints, while minimizing a cost function

such as spanned image area, trajectory length and curvature.

1.2.2.2 Position-Based Visual Servoing Schemes

The position-based visual servoing approach is also called 3D visual servoing be-

cause the control inputs are computed in the three dimensional Cartesian space. The

pose of the target with respect to the camera is estimated from image features. To

do that, a perfect geometric model of the target model and a calibrated camera are

6 1 Introduction

required. Results in computer vision about 3D reconstruction from two views have

been applied successfully, making the knowledge of the object model unnecessary,

however the calibration requirements cannot be avoided. The position-based visual

control approach has been applied mainly for robot manipulators. Usually, a pose-

estimation technique is used to recover the Cartesian required information. In [142],

an extended Kalman ﬁlter-based estimation is used to design a control law in terms

of relative positions between the end-effector and the target object. In [80], adaptive

Kalman ﬁltering techniques are explored to improve the precision of the estimation

in position-based visual servoing for manipulators [127]. Two papers introduce vi-

sual servoing based on an observer-scheme for applications with manipulators [62],

[64]. A visual tracking scheme that includes a kinematic model for the object to

be tracked is used. To perform the visual servoing task, the authors of [103] use a

nonlinear state feedback. They propose an exact model for parametrization of the

pose that allows the control of the translation and rotation of the camera separately.

This work attempts the common concern of visual control approaches to design de-

coupled schemes. Another concern of visual control is to keep the image features

belonging to the target in the current view along the navigation. In [135], a position-

based visual servoing approach that consists in tracking an iteratively computed

trajectory is designed to guarantee that the target object remains in the ﬁeld of view.

Currently, the research on visual control focuses on applications on monocular

vision and the use of stereo vision has received less attention. An approach that

strictly speaking is a position-based visual servoing scheme takes advantage of the

3D features provided by a stereo vision system [28]. 3D coordinates of any point

observed in both images can be easily estimated by a simple triangulation process.

Binocular vision has proved the beneﬁt of robustness to calibration errors exploiting

optical ﬂow [58]. Alternative feature vectors combining 2D and 3D information

from a stereo system have been proposed in [27]. That work shows that point depth

and object pose produce an improved behavior in the control of the camera.

It is worth mentioning that both image-based and position-based visual servoing

exhibit potential problems of stability [29], and only local stability can be theoreti-

cally demonstrated. In the case of image-based visual servoing it is due to the rect-

angular form (in general) of the interaction matrix that has a no trivial null space. In

the case of position-based visual servoing any error in the estimation of the pose pa-

rameters required in the interaction matrix affects the stability property of the closed

loop.

1.2.3 Visual Servoing through a Geometric Constraint

The classical visual control schemes use a batch of features directly extracted

from the images to compute the error function. Another option to extract useful

information in order to control a robot from monocular images is by means of ge-

ometric constraints that relate two or three views. Geometric constraints are im-

posed in the images when there are correspondences between features [60]. At

present, three constraints are well known in computer vision and have been used for

1.2 State of the Art on Visual Control 7

control purposes: the homography model, the epipolar geometry and the trifocal

tensor. The use of geometric constraints has given origin to hybrid schemes that

improve the performance of classical image-based visual servoing. In [48], the ho-

mography and the epipolar constraint are used to generate the optimal trajectory of

the robot motion to reach the goal straightforwardly with decoupled translation and

rotation. The 2-1/2D visual servoing which is based on the estimation of the partial

camera displacement from the current to the desired camera poses at each iteration

of the control law is proposed in [96]. This scheme does not need any geometric 3D

model of the object as required in position-based visual servoing, and it ensures the

convergence of the control law in the whole task space, unlike image-based visual

servoing. An outstanding work in the hybrid visual control approach concerns about

the stability analysis of a class of model-free visual servoing methods that can be

hybrid or position-based visual servoing [95]. In any of both cases, these methods

do not need a 3D model of the target object. Additionally, the visual servoing is

decoupled by controlling the rotation of the camera separately from the rest of the

system. In [34], a homography-based adaptive visual servo controller is developed

to enable a robot end-effector to track a desired Euclidean trajectory as determined

by a sequence of images. The error systems are constructed as a hybrid of pixels in-

formation and reconstructed Euclidean variables obtained by comparing the images

and decomposing a homographic relationship.

A homography-based approach for image-based visual tracking and servoing is

proposed in [23]. The visual tracking algorithm is based on an efﬁcient second-order

minimization method and its output is a homography linking the current and the ref-

erence image of a planar target. Using the homography, a task function isomorphic

to the camera pose is designed, and thus, an image-based control law is proposed. In

[35], an image-space path planner is proposed to generate a desired image trajectory

based on a measurable image Jacobian-like matrix and an image-space navigation

function. An adaptive homography-based visual servo tracking controller is then de-

veloped to navigate to a goal pose along the desired image-space trajectory while

ensuring that the target points remain visible.

In order to avoid the largely over-constrained control commands resulting in

monocular approaches, in [75], the authors propose to exploit explicitly the epipolar

constraint of two stereo images. A hybrid switched-system visual servo method that

utilizes both image-based and position-based visual servoing is presented in [54].

The switching strategy achieves stability in both the pose space and image space si-

multaneously. With this strategy is possible to specify neighborhoods for the image

error and pose error that the state can never leave. In [13], the epipolar constraint is

introduced for visual homing of robot manipulators. By using the epipolar geome-

try, most of the parameters (except depth) which specify the differences in position

and orientation of the camera between the current and target images are recovered.

The method is memoryless, in the sense that at every step the path to the target po-

sition is determined independently of the previous path. In [118], a visual servoing

based on epipolar geometry for manipulators is reported. It discusses how the real

value of the translation to be reached is unpredictable and proposes a control scheme

which decouples the control of the rotation and the translation using the projective

8 1 Introduction

properties of the fundamental matrix. Additionally, The epipolar visual control has

become in a powerful approach for mobile robots as will be described later.

The ﬁrst work that proposes a robotic application of a trilinear constraint is [49].

The trifocal tensor has proved its effectiveness to recover the robot location in [59].

The onedimensional version of the trifocal tensor has been also proposed for hierar-

chical localization with omnidirectional images in [110]. Recently, the trifocal ten-

sor has been introduced for visual servoing of robot manipulators in [126]. Schemes

using higher order tensors with more than three views have been explored for visual

odometry [38].

1.2.4 Robust Visual Servoing

Another important issue in visual servoing concerns for uncalibrated methods. Some

good results toward the development of robust visual techniques used to guide

robots in several real-word tasks are presented in [74]. The scheme attempts to keep

the object in the ﬁeld of view, or even centered, while the end-effector is approach-

ing to it. A visual servoing scheme which is invariant to changes in camera-intrinsic

parameters is presented in [93]. With this method, it is possible the camera posi-

tioning with respect to a nonplanar object given a reference image taken with a

completely different camera. A dynamic quasi-Newton method for uncalibrated vi-

sual servoing that estimates the composite Jacobian at each step is used in [115].

An adaptive controller for image-based visual servoing using a ﬁxed camera whose

intrinsic and extrinsic parameters are unknown is presented in [81]. It proposes a

depth-independent interaction matrix and estimates on-line the values of the un-

known parameters. The results in [140] present an adaptive scheme that avoids the

dependence of the scheme on depth information.It exploits the dynamics of manipu-

lators to prove asymptotic convergence of the image errors. However, this approach

needs additional feedback of the robot state (position and velocity). Additionally,

the camera calibration parameters are estimated on-line using a bundle adjustment

strategy that is sensitive to initial values.

Few efforts have been done to take some robust control techniques for vision-

based feedback. One of this techniques that is well know for its property of robust-

ness is the sliding mode control. This control technique provides the possibility to

deal with parametric uncertainty due to weak camera calibration. On one hand, slid-

ing mode control has been used for 3D trajectory tracking with a position-based

visual servoing scheme through a pose reconstruction algorithm [144]. On the other

hand, sliding mode control has been proposed for 6 degrees of freedom image-based

visual servoing in [73], and recently combined with a pre-estimation of the robot

state [78].

1.2.5 Omnidirectional Visual Servoing

One effective way to enhance the ﬁeld of view of conventional cameras is to

use mirrors in conjunction with lenses, i.e., catadioptric image formation systems.

1.2 State of the Art on Visual Control 9

The authors of [12] propose to use catadioptric cameras to observe the whole robot’s

articulated mechanism so that its joints can be tracked and controlled simultane-

ously. It has been shown that some results of stability and robustness obtained for

conventional cameras are extendable to the entire class of central catadioptric sys-

tems [108]. For instance, some of these extensions are the 2-1/2D scheme of [2] and

the path planning strategy proposed in [4].

The problem of controlling a robot from the projection of 3D straight lines in the

image plane of central catadioptric systems is addressed in [5]. A generic interaction

matrix for the projection of 3D straight lines is derived using the unifying imaging

model [56]. A new decoupled image-based visual servoing scheme allowing the

control of translational motion independently of rotation is proposed from the pro-

jection onto a unitary sphere in [132]. The scheme is based on moments that are

invariant to 3D rotational motion. The homography model has been also exploited

for omnidirectional visual servoing of 6 degrees of freedom. The authors of [22]

propose an image-based control law that minimizes a task function isomorphic to

the camera pose. They provide the theoretical proofs of the existence of the isomor-

phism and the local stability of the control law. Other geometric constraints have

been exploited while using omnidirectional vision for visual servoing, particularly

focused on the control of mobile robots, as detailed in the next section.

1.2.6 Visual Control of Mobile Robots

From the last decade, some Jacobian-based visual servoing schemes for mobile

robots have been proposed as an extension of those schemes for 6 degrees of free-

dom, for instance [104], [136]. These works propose to add some degrees of free-

dom to the mobile platform by acting the camera to overcome the control issues

related to the non-holonomic constraint of wheeled robots. This is avoided in [63],

where two visual cues attached on the environment are controlled through an image-

based visual servoing scheme that linearizes the dynamics of the non-holonomic cart

transformed into the image plane. These image-based visual servoing schemes are

sensitive to noise and wrong corresponding point features, and often, it is required to

apply some robust ﬁltering technique for smoothing and matching visual measure-

ments [39]. Redundancy resolution methods have been employed for image-based

visual servoing of non-holonomic mobile manipulators [89]. An strategy for visual

motion planning in the image space is presented in [145].

Most of the visual servoing schemes have the drawback that the target may leave

the camera ﬁeld of view during the servoing, which leads to failure because the

feedback error cannot be computed anymore. Some position-based visual servoing

schemes have been proposed to avoid this problem. For instance, the switching con-

troller of [53] uses an Euclidean homography-based reconstruction to estimate the

robot pose. The parking problem with limited ﬁeld of view is tackled in [111] with a

switching control law, whose stability is analyzed through the theory of hybrid sys-

tems and the robot pose is estimated in closed form from the motion of the image

features.

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