Chapter 5. Advanced Bayesian Estimation in Semi-Autonomous Wheelchair
5.2. Semi-autonomous Wheelchair Control Strategy
5.2.3. Semi-autonomous Wheelchair Control
5.2.3.1. Bayesian Estimation for Intention of the User
The semi-autonomous wheelchair control system represents the combination of the user intention and the autonomous mode, in which the user intention is the control of the user through the user’s intentions and the autonomous mode is the autonomous control.
However, the user’s intentions can be uncertain due to head sensor noise or weak provided by individuals with severe disabilities. For this reason, an advanced BR algorithm is applied in the semi-autonomous control to estimate user intentions and the decision for the wheelchair’s motion is generated based on optimal probabilities.
In order to apply the BR algorithm for intention estimation of the user, assume that the user’s intentions, uuser for turning left and right, or controlling forward and backward is a head-movement model as shown in Figure 5.15. The user can override the wheelchair a control command to smoothly pass through freespaces or to avoid obstacles. A range
Chapter 5. Advanced Bayesian Estimation in Semi-Autonomous Wheelchair Control
of degrees is assigned from(a1÷a2) for the right turning and (b1÷b2) is the similar range for the left turning. The similar ranges are (c1÷c2) and (d1÷d2) for controlling forward and backward.
00
900
900
−
a1
ng
Left turni Right turning
a2
b1
b2
X
00
900
900
−
d1
g controllin Forward
d2
c1
c2
Y g
controllin Backward
Figure 5.15: head commands using a head sensor are ranges of degrees, (a1÷c2) and (b1÷b2) for left and right turning; (c1÷c2) and (d1÷d2) for controlling forward and backward
We can define the ranges of degrees for the user intention and the autonomous mode in the semi-autonomous wheelchair control for the wheelchair’s operation in populated environments. Assume that the ranges of the degrees corresponding to the user’s intentions using the head sensor to control the wheelchair to reach the desired target are (a1÷a2) and (b1÷b2) as well as (c1÷c2) and (d1÷d2). Therefore, the wheelchair using the autonomous mode, which can autonomously move through freespaces or avoid obstacles without using the head commands, has the degree ranges of (a1÷a2) and (b1÷b2) and (c1÷c2) and (d1÷d2).
The case is that if the tilt angle of the head movement of the user is in the defined intervals, the wheelchair can operate with the user intention uuser(ωu,vu). However, this is difficult for the disabled people to control the mobile wheelchair to reach the desired target through a head-movement sensor, so the user’s intentions are uncertain and weak.
For this reason, an advanced BR algorithm is applied to estimate intention state of the user in the semi-autonomous wheelchair control which is combined between the user intention and the autonomous mode in populated environments. In particular, if the tilt angle is out of the defined intervals, the wheelchair’s operation should be installed the autonomous mode uauto(ωa,va) so that the wheelchair can autonomously pass through freespaces or avoid possible collisions.
Chapter 5. Advanced Bayesian Estimation in Semi-Autonomous Wheelchair Control
Before representing mathematical formulas of intention state estimation, probabilistic laws related to measurements and freespace estimation in the Bayesian estimation of the semi-autonomous wheelchair control strategy are described. The measured data zct are obtained from the head-movement sensor. In a populated environment, pfs,t(Wd1-t, udt-1, zd1-t, hobs1-t) is the history of the freespace estimation, including all freespace states (Wd1:1-t= {Wd1,…, W d1-t}), all width measurements (zd1:1-t= {zd1,…, zd1-t}), all wheelchair controls (ud1:1-t= {ud1,…, ud1-t}) and all “obstacle” distances (hobs1:1-t= {hobs1,…, hobs1-t}).
The freespace estimation over the intention state Ct is defined as follows:
⎩⎨
⎧ = > =
= for otherwise ) (
) (
for
1 2
OB
OB w P FS w P
pfst FS av av (5.16a)
fst fs
fs fs t
fs p p p p
p 1: = 1, 2, 3,K, (5.16b)
) ,
| ( ) , ,
|
(Ct C0:t 1 zc1:t 1 hobs1:t p Ct Ct 1 hobst
p − − = − (5.16c)
Assume that the intention state Ct is complete based on Ct-1 is a previous state of all past freespace estimation and measurements pfs1:t-1 and zc1:t-1. In this case, the conditional probability is equally expressed as follows:
)
| ( ) , ,
|
(zct Ct zc1:t 1 pfs,1:t p zct Ct
p − = (5.17)
However, the conditional probabilities often has errors due to noise from the head sensor or disabled people.
The posterior probability based on the previous probability and the history of freespace estimation pfst over the previous intention state Ct-1 at the previous time t-1 is described as follows:
∑ = =
=
= − −
k
k t po k t fst t i
t
pr C c p C p C c P C c
P ( ) ( | , 1 ) ( 1 ) (5.18)
in which the state Ct, which can take on, is discrete and the sum of the posterior probabilities is∑ ( = )=1
i
i t
pr C c
P with the state Ct=ci, for ci=c1, c2, … and ck=c1, c2, ….
Chapter 5. Advanced Bayesian Estimation in Semi-Autonomous Wheelchair Control
The optimal probability is the posterior probability distribution over the intention state Ct at the time step t. The optimal probabilities Ppo(Ct) the posterior probability Ppr(Ct) and head sensor measurements zct are expressed as follows:
∑ = =
=
=
k ct t k pr t k
t pr t ct i
t
po p z C c P C c
C P C z c p
C
P ( | ) ( )
) ( )
| ) (
( (5.19)
in which the sum of probabilities in the Bayesian rule is ∑ ( = )=1
i
i t
po C c
P with the
state Ct=ci, for ci=c1, c2, … and ck=c1, c2, ….
In practice, there are many kinds of different signals obtained from body sensors such as voice, brain, face’s gesture and head-movement which can be continuous. In this case, the posterior probability using the advanced BR algorithm applied to estimate signal states can be described as follows:
dC C P C p C p C
Ppr( t)=∫ ( t| fst, t−1) po( t−1) (5.20)
The optimal probability Ppo(Ct) based on the posterior probability and the previous state Ct-1 can be expressed as follows:
) ( )
| ( )
( t = ct t pr t−1
po C p z C P C
P η (5.21)
in which η is the normalized coefficient.
In this section, the state is the user’s intentions using the head-movement sensor. The intention state in the advanced BR algorithm is discrete and assigned for two possible cases including the user intention and the autonomous mode. To be more specific, if the intention state is of the user, the state is assigned c1=uuser, otherwise the state is c2=uauto, if the intention state is estimated to be of the autonomous mode. Therefore, the advanced BR algorithm will produce two posterior probabilities including the user probability P(Ct=uuser) and the probability of the autonomous mode P(Ct=uauto) which are used to make the Bayesian decision for the wheelchair’s motion in the semi- autonomous wheelchair control.
Chapter 5. Advanced Bayesian Estimation in Semi-Autonomous Wheelchair Control