Abstract Online evaluation of battery State of Function
(SOF) is crucial for battery management systems of autonomous
mobile robots. Battery State of Charge (SOC) represents its
remaining energy available, whereas internal resistance and
capacity reflect its State of Health (SOH). In this paper, an
improved equivalent circuit model is proposed to estimate SOC,
internal resistance and capacity using an Unscented Kalman
Filter (UKF). The proposed method not only estimates SOC, but
also evaluates SOH and SOF. Experimental results have shown
the effectiveness of the proposed method using resistive loads
and a robot prototype for inspecting power transmission line.
I. INTRODUCTION
In the last few years, Autonomous Mobile Robots (AMRs)
have found many applications in high-risk and unstructured
environments, such as inspection of power distribution lines.
As such robots rely heavily on the power capability of the
battery onboard, it is important that the battery is reliable and
capable of delivering enough energy or power when it is
required. State of Charge (SOC) and State of Health (SOH)
are two important features to evaluate the State of Function
(SOF) of a battery [1]. The SOC can be regarded as the ratio
of the stored charge available relative to that available after a
full charge of a battery. It directly indicates the residual
energy of a battery, and indirectly indicates the operation
scope of an AMR. A variety of algorithms have been
proposed to estimate SOC [2], such as Coulometric
measurement, electrolyte specific gravity, stabilized float
current, open circuit battery voltage, and loaded battery
voltage. The SOH deals with the estimations of end of life,
capacity fading and increase of internal resistance of a
battery.
Aging causes undesirable effects on battery, deteriorating
the battery SOH and the performance of the AMR that the
battery powers. Battery manufacturers define the end of a
battery life as when the battery only delivers up to 80% of its
rated amp-hour capacity. After that, if the battery continues to
be used, its performance would decay drastically [3]. Besides,
with increase of its internal resistance, the battery may fail to
supply enough current or power to the AMR.
Manuscript received September 9, 2008. This work was supported in part
by the National High Technology Research and Development Program of
China under Grant 2006AA04Z203.
F. Zhang is with the State Key Laboratory of Robotics, Shenyang Institute
of Automation, Chinese Academy of Sciences, Shenyang, China 110016 (Tel:
(86)24-23970237; Fax: (86) 24-23970021;E-mail: zhangfei@sia.cn).
G. Liu is with the Department of Aerospace Engineering, Ryerson
University, Toronto, Canada M5B 2K3 (E-mail: gjliu@ryerson.ca).
L. Fang is with the State Key Laboratory of Robotics, Shenyang Institute
of Automation, Chinese Academy of Sciences, Shenyang, China 110016
(E-mail: ljfang@sia.cn).
In [3], the effect of Coup de Fouet is used to estimate the
capacity for a valve regulated lead acid battery by considering
that the relationship between the capacity and the trough
voltage is determinate, which limits practical applications of
the method, because this relationship varies from battery to
battery. In [4], based on the relationship between
conductance and capacity, the capacity is estimated through
measuring the conductance. In order to measure the
conductance, a signal has to be injected into the battery,
making the method unsuitable for an AMR. In [5], an
Extended Kalman Filter (EKF) is applied to estimate battery
capacity, considering the reciprocal of the capacity as a
system state. In [6-7], based on a simplified circuit model,
battery internal resistance is estimated with a Kalman Filter
(KF). In [8], internal resistance is estimated by calculating the
noise intensity of electrochemical reactions. However, this
method needs special equipment to measure the noise. In
order to avoid the requirement that the system is observable, a
method is proposed in [9] to estimate capacity and internal
resistance using the moving-horizon parameter estimation.
For evaluating battery SOF in an AMR, SOC, internal
resistance and capacity need to be estimated. On the one hand,
compared with the change rate of the internal resistance, the
change rate of the capacity is much slower in an AMR, thus
the internal resistance can be estimated through treating the
capacity as a constant. On the other hand, because of the very
slow change rate of the capacity, it is not necessary to
estimate it in real-time. Thus the capacity can be estimated
when the AMR stops, in order to reduce the system
calculation overhead. When the AMR stops, battery current
can be considered smooth, the capacity can be estimated by
considering the internal resistance constant. As a result, the
internal resistance and capacitance indicating the battery
capacity can be estimated separately in an AMR.
In this paper, an improved equivalent circuit model is
proposed for estimating battery SOC, internal resistance, and
capacity using an Unscented Kalman Filter (UKF). SOC is
obtained through estimating battery open circuit voltage. The
internal resistance is estimated by treating the capacity as a
constant. The capacity is estimated by considering the
internal resistance constant. The proposed method not only
estimates battery SOC, but also evaluates its SOH and SOF.
Some experiments have been conducted using resistive loads
and a robot prototype for inspecting power transmission line.
Experimental results have shown the effectiveness of the
proposed method.
The rest of this paper is organized as follows. In Section II,
an improved equivalent circuit model is proposed to estimate
Battery State Estimation Using Unscented Kalman Filter
Fei Zhang, Guangjun Liu, Senior Member, IEEE, and Lijin Fang
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