动态反馈线性化在无障环境下的轮式移动机器人控制：设计与实验验证

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本文档探讨的主题是"动态反馈线性化在自主移动机器人（Autonomous Mobile Robots）中的无线电机车（Wheeled Mobile Robots, WMRs）控制问题"。作者Giuseppe Oriolo和Alessandro De Luca，均为IEEE成员，以及Marilena Vendittelli共同研究了一种创新的控制策略，它基于动态反馈线性化理论，该理论在无障碍物环境中的WMRs运动轨迹跟踪和设定点调节问题上提供了一种有效的设计工具。 "IEEE Transactions on Control Systems Technology"第10卷第6期的论文中，作者详细介绍了这一设计方法如何将传统的双轮差动驱动移动机器人（如实验室原型Super Mario）的非线性和非holonomic特性转化为线性系统，从而简化了控制器的设计过程。通过这种方法，控制器能够同时处理多种任务，提高了系统的灵活性和效率。为了验证这种设计的有效性，作者在一系列实验中对比了所提出的控制技术与其他现有控制方法的性能。这些实验结果不仅提供了对WMR控制系统设计的重要参考，还揭示了动态反馈线性化在实际应用中的优势，如稳定性、响应速度和准确性等关键指标。对于那些专注于WMR控制领域的研究人员和工程师来说，这篇论文不仅阐述了理论概念，还提供了实用的工程实践指导，有助于推动该领域的技术进步。因此，理解并掌握动态反馈线性化在WMR控制中的应用，对于提升移动机器人的自主导航和路径规划能力具有重要意义。

838 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 10, NO. 6, NOVEMBER 2002

(butno necessary and sufficient)conditions existfor the solution

of this problem. Constructive algorithms are essentially based

on input-output decoupling [22].

The starting point is the definition of an

-dimensional

output

, to which a desired behavior can be assigned.

One then proceeds by successively differentiating the output

until the input appears in a nonsingular way. At some stage,

the addition of integrators on some of the input channels

may be necessary to avoid subsequent differentiation of the

original inputs. This dynamic extension algorithm builds up

the state

of the dynamic compensator (6). If the system is

invertible from the chosen output, the algorithm terminates

after a finite number of differentiations. If the sum of the

output differentiation orders equals the dimension

the extended state space, full input–state–output linearization

is obtained.

The closed-loop system is then equivalent to a

set of decoupled input–output chains of integrators from

We illustrate this exact linearization procedure for the uni-

cycle model (1). Define the linearizing output vector as

. Differentiation with respect to time then yields

showing that only affects , while the angular velocity

cannot be recovered from this first-order differential informa-

tion. To proceed, we need to add an integrator (whose state is

denoted by

) on the linear velocity input

being the new input the linear acceleration of the unicycle.

Differentiating further, we obtain

and the matrix multiplying the modified input is nonsin-

gular if

. Under this assumption, we define

so as to obtain

(7)

The resulting dynamic compensator is

(8)

Being

,itis , equal to the output

differentiation order in (7). In the new coordinates

In this case,



is also called a flat output [25].

Fig. 3. WMR SuperMARIO.

(9)

the extended system is, thus, fully linearized and described by

the two chains of integrators in (7), rewritten as

(10)

The dynamic compensator (8) has a potential singularity at

, i.e., when the unicycle is not rolling. The occur-

rence of such singularity in the dynamic extension process is

structural for nonholonomic systems [6]. This difficulty must

be obviously taken into account when designing control laws

on the equivalent linear model.

IV. T

ARGET VEHICLE:SUPERMARIO

The experimental validation of the proposed control method

and its comparison with existing controllers has been performed

on our prototype SuperMARIO (Fig. 3).

A. Physical Description

SuperMARIO is a two-wheel differentially driven vehicle.

The wheels have a radius of

cm and are mounted on an

axle

cm long. The wheel radius includes the o-ring used

to prevent slippage; the rubber is stiff enough that point con-

tact with the ground can be assumed. A small passive caster is

placed in the front of the vehicle at 29 cm from the rear axle. The

aluminum chassis of the robot measures 46

32 cm

(l/w/h) and contains two motors, transmission elements, elec-

tronics, and four 12-V batteries. The total weight of the robot

is about 20 kg and its center of mass is located slightly in front

of the rear axle. This design limits the disturbance induced by

sudden reorientation of the caster. Each wheel is driven by an

MCA dc servomotor supplied at 24 V with a peak torque of

0.56 Nm. Each motor is equipped with an incremental encoder

counting

pulses/turn and a gearbox with reduction

ratio

. On-boardelectronics multiplies by a factor

the number of pulses/turn, representing angular increments with

16 bits.

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