Reaching Analysis of Wheelchair Users
Using Motion Planning Methods
Jing Yang, Michael Jenkin and Patrick Dymond
{jyang, jenkin, dymond}@cse.yorku.ca
Department of Computer Science and Engineering, York University, Toronto, Canada
The Problem
A high dimensional search problem
Computationally intractable problem
Can a wheelchair user reach
critical devices, such as
light switches, electrical
outlets and other
environmental controls?
- Problem is exponential to the degree of freedom
(DoF) of the device (here 7 DoF for the
wheelchair user)
- Naive probabilistic solutions are expensive and
often identify impractical (high cost) solutions
Underlying Computational Problem
Kinematic model
of wheelchair user
Environmental
model
Wheelchair: 3 DoF
Arm: 4 DoF
Initial state
Goal location
Rapidly-exploring
Random Tree (RRT)
Algorithm
1. Build the RRT rooted from the start
configuration
2. Repeatedly grow the tree towards a
random direction until the goal is reached.
Start
A motion planner takes
these properties to
identify a collision-free
and practical path from
the start state to the goal
Collision-free path
RRT or
RRTGoalRegionBias
RRTGoalRegionBias
Reaching Analysis of Wheelchair Users
3
z1
φ3
Motivations
- The movement of the arm is
'secondary' to that of the wheelchair
- The motion of the wheelchair user
can be decomposed into motion of the
wheelchair and motion of the arm
φ1
x1
O1 φ2
y1
z
Shoulder joint
y2 z2
x2
y
φ4
O2
θ
(x, y)
O0
x0
A path computed by RRTGoalRegionBias
takes the wheelchair to the goal more directly
(b)
(c)
Algorithm
developed a method based on a Probabilistic Roadmap Method (PRM) to hierarchically
1. Generate a potential
goal
region
maximize
the reachability
of each configuration in the PRM. A kinematic model was
created based on a robotic wheelchair that comprised a mobile base and an attached
around the point of interest
manipulator with 4 revolute joints. In this paper we consider only the problem of reachability and exploit properties of the task and the kinematic properties of a mobile base
the process
of searching for
paths in this complex high dimensional space.
2. Bias the growth ofto optimize
RRT
towards
the
C
potential goal reaching
region
3 Formal
statement of the problem
Goal
goal
In its most general form, the problem of the wheelchair reaching analysis involves finding a feasible motion for the wheelchair and user from some starting configuration to
reach a goal point. We define the following properties of the problem in terms of the
motion planning notation.
Performance
Comparison
8
Author 1 and
Author 2
Problem
A path computed by the RRT contains many
zig-zags and unnecessary motions of the arm
Wheelchair center
Fig. 1. (a) Kinematics of the person sitting in a wheelchair, whose configuration can be written as
(x, y, θ, φ1 , φ2 , φ3 , φ4 ). (x, y, θ) specifies the pose of the wheelchair, and (φ1 , φ2 , φ3 , φ4 ) specifies
Start
the pose of the arm relative to the wheelchair frame. (b - c) Illustration of the reachable
sphere of
the wheelchair user shown in the green area.
Experimental Validation
Motion Demonstrations
O
r
y0
(a)
Advantages
- Efficient for high-dimensional and complex problems
- Probabilistic completeness
Limitations
- Slowly reach the goal since the tree expands in all
directions in the search space
O
x
z0
Elbow joint
Goal
r
(start → goal)
RRT
# Success
RRTGoalRegionBias
RRT
# Nodes
RRTGoalRegionBias
RRT
Path Length
RRTGoalRegionBias
3.1
Environmental model and kinematic model
The environmental model is a three-dimensional static Euclidean space W that needs
to be accessible to wheelchair users. W has a flat ground . Some portions of W are
obstacles
workspace).
denote
model
the desired
c1 → p1 occupied
c2 →(there
p1 arec3
→ p1in thec1
→ p2 Letc2A→
p2the c3
→ofp2
kinematic structure. A consists of a mobile wheelchair base Abase and an attached kine38 matic chain
40 that models30
32
46
human’s arm A27
arm . To simplify the problem we only consider
arm in this paper,
100 the right
100
85 but the method
91 can easily be87extended to two
80arms. A configuration of A is a specification of the position of every point in A relative to the global
10308 Cartesian
12267
11527 of A , 10381
frame W .11261
Given the configurations
the position and9941
orientation of the
can easily be determined
kinematics 7825
of A .
3556 hand 3930
5938 by computing
7451 the forward
6708
665
657
860
826
921
901
739
731
843
799
837
845
- Performance
statistics
averaged
for
Table 1. Performance statistics for various
problem sets. Results
are averaged
for 100 indepenc2each case.
dent runs for
100
independent
runs
for
each
case
c3
c1
- RRTGoalRegionBias has better
p2
success
rate
and
is
more
efficient
than
p1
model of a person sitting in a wheelchair and an efficient motion planner. The motion
the RRT
planner is based on RRT, which generates
a potential goal region based on the point to
reach (that requires analysis) first -and
then
uses
this
region
to
bias
the
RRT
to
find
a
path.
RRTGoalRegionBias can find paths
The current developed tool provides a visual display for the clinicians to gain better
comparable
exhaustive
RRTshow
understanding of the wheelchair’s
performance into
thethe
workspace.
Experiments
that our RRTGoalRegionBias planner is more efficient and effective than the existing
RRT planner to find a path.