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An Efﬁcient Path Planner for Large Mobile

Platforms in Cluttered Environments

Tarek Taha, Jaime Valls Mir´

o and Dikai Liu

ARC Centre of Excellence for Autonomous Systems

Mechatronics and Intelligent Systems Group

University of Technology Sydney

NSW2007, Australia

{t.taha, j.vallsmiro, d.liu}@cas.edu.au

Abstract— This paper presents a one step smooth and efﬁcient

path planning algorithm for navigating a large robotic platform

in known cluttered environments. The proposed strategy, based

on the generation of a novel search space, relies on non-uniform

density sampling of the free areas to direct the computational

resources to troubled and difﬁcult regions, such as narrow

passages, leaving the larger open spaces sparsely populated. A

smoothing penalty is also associated to the nodes to encourage the

generation of gentle paths along the middle of the empty spaces.

Collision detection is carried out off-line during the creation of

the conﬁguration space to speed up the actual search for the path,

which is done on-line. Results prove that the proposed approach

considerably reduces the search space in a meaningful and

practical manner, improving the computational cost of generating

a path optimised for ﬁne and smooth motion.

I. INTRODUCTION

The problem of computing a collision-free path for a

moving object among obstacles is well known in the ﬁeld of

robotics, and has been an active research topic for decades [4].

The majority of the proposed algorithms transform the problem

into a pure geometric path planning problem by deﬁning the

search in what is known as conﬁguration space, or C-space,

an approach originally introduced by Lozano-Perez [2], [5].

Here, a robot with kdegrees of freedom can be described by

kvalues, which can in turn be considered as a single point

in a k-dimensional C-space of the robot. This conﬁguration is

considered free if two parts touch and blocked when two parts

overlap. For mobile robots operating in ﬂat ground, C-space is

usually deﬁned as a set of all possible conﬁgurations encoding

the position and orientation of the vehicle. A collision free

feasible path is that connecting the start and goal point

conﬁgurations. Also, a holonomic characteristic is normally

assumed, which holds for the case of differential-drive robots

like a wheelchair.

The exact construction of the C-space is however a com-

putationally expensive solution to the path planning problem.

The need to move away from complete path planning algo-

rithms inspired the development of sampling-based techniques.

Hence, the majority of techniques make further assumptions

and construct approximate representation of the C-space using

sampling-based techniques. These techniques provided a faster

practical solution by sacriﬁcing completeness, in which a set

of sampling points are used to represent the C-space that is

used in constructing solutions. Traditionally, sampling-based

algorithms are based on uniform sampling which considers

the whole environment as uniformly complex and thus the

overall sampling density will be equivalent to the density

needed by the most complex region. The result is that every

region in the C-space has the same computational complexity,

reaching its worst case when narrow passage areas exist in the

environment [1]. Furthermore, paths produced by randomised

planners usually contain non-smooth segments because of this

randomness and the absence of optimisation criteria.

For the problem of navigating large robots in narrow and

cluttered environments, such as as ”intelligent” wheelchairs

in the average home surroundings, conventional path planning

algorithms based on free C-space construction also tend to fail:

in order to be able to consider the robot as a k-dimensional

point, they generally expand the obstacles in an over-simplistic

manner by the length of the larger robot dimension, which very

often will prevent reaching a solution even when it exists [5].

In this paper we propose a hybrid path planning algorithm

inspired by the C-space approach, where we avoid the com-

putational complexity of generating a denser search area by

employing a non-uniform sampling density: this is increased

in complex areas, leaving simple areas with lower resolution

density, hence directing computational resources towards the

complex areas, also know as narrow passages. A reduction of

the information embedded in the C-space, and a smoothing

cost function are also introduced to generate smoother paths

in an efﬁcient manner. The algorithm takes further advantage

of techniques like the bridge test [3] and an optimised obstacle

expansion method to further reduce the number of samples and

the points to be check for obstacle collision. A modiﬁed A*

search is then implemented to ﬁnd suitable paths on this space.

The remainder of this paper is organised as follows: latest

proposals to the path planning problem and where our ap-

proach represents an improvement for the problem at hand is

analysed in-depth in Section II. The proposed methodology

for the creation of the search space is presented in Section III,

with Section III-A.5 explaining the non-uniform random dis-

cretisation. Section III-B summarises the customisations to the

A* graph search technique to take advantage of the search

framework proposed here. Detailed experimental setup and

c

2006 IEEE RAM 2006

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connecting distance, and the computational complexity: shorter

distances between the nodes will result in fewer angular and

position discretisations (fewer neighbours) and less impact

on computation, but might decrease the possibility of ﬁnding

a path. On the other hand, longer distances will produce a

larger number of connections, hence increasing the chances of

ﬁnding a solution at the expense of complexity. A reasonable

compromise is to connect nodes with a distance equivalent

to the distance used to sample the uniform regular grid. This

ensures continuity in node connections and at the same time

results in a faster search.

6) Collision Detection: Finally, those connections that

cause a collision of the platform with the obstacles are elimi-

nated. The connections between nodes determines the possible

orientations of the robot should it follow that path. The center

of the circles that describe the area of the robot along that path

can be rotated and translated accordingly. Hence we can then

determine if any of them falls into an occupied area or not,

removing those conecting nodes that will cause a collision.

The result will be a collision free search space of connected

nodes in which to efﬁciently carry out the on-line search for

a path.

B. On-line Path Planning

The A* path planning algorithm [13] is a well known

technique, well regarded for its accuracy and calculation speed

in searching for an optimal solution. A* works by exploring

nodes based a cost function which is the sum of g(n), the

cost from the start node to node n, and the estimated cost

from node n to the goal h(n). It uses an heuristic search to

estimates the cost to the goal node and minimises the cost of

the path so far. A* is optimal if the estimated cost to the goal

is always underestimated. Since the shortest distance between

two points is a straight line, euclidean distance serves as an

excellent estimated cost to goal, making A* well suited for fast

computations. In the algorithm proposed here, the cost function

J(d)combines the sum of the partial path distances ∆d,the

sum of all the distances travelled as a result of changing

orientation ∆θx where xis the length of the axis of the rear

wheels, the sum of the clearance penalties previously computed

ofﬂine - which is directly proportional to the distance ∆d- and

the number of reversals (backward motion) in the path nrev.

The cost function, deﬁned as follows:

J(d)=∆d+∆θx+∆dC

p+nrev (3)

encourages the robot to avoid whenever possible turns and

reversing actions, while at the same time directing it towards

the middle of free space. The result is a smooth and secure

path - in the context of the obstacles around the platform -

efﬁciently generated in a single step.

IV. EXPERIMENTAL RESULTS

In order to compare the efﬁciency of the proposed al-

gorithm, we ﬁrst compare the performance of a traditional

uniform regular sampling C-space with our random non-

uniform sampling approach for a simple navigation problem.

Fig. 4. Uniform sampling: the whole environment is equally mapped with a

constant density of search nodes

Fig. 5. Non uniform sampling: density is increased around tight places,

leaving open spaces with a lower number of search nodes

The simulations were carried out in a PC with a 1.8 GHz

Pentium IV processor and 512 Mb RAM. A map of size

45x20mwas discretised uniformly by 0.1mto generate the

search space, a detailed section of which is shown in Figure 4,

where white spaces represent the obstacles in the map after

having bee expandedn. This is the same density employed

to discretised the tight passages with the non-uniform sample

method proposed here, where a bridge test with 2mlength was

exercised. The resulting search map is that depicted in Fig-

ure 5, where a 0.2muniform sampling density was employed

for the open spaces. In both cases the obstacle expansion was

set to 0.2m, and the starting and goal conﬁgurations were the

same. Search technique was also the same in both cases, so that

the ﬁnal paths produced were expectedly similar, as seen by

the sequence of rectangles which represent the conﬁgurations

of the wheelchair at each step on the planned paths based

on the wheelchair footprint. However, the comparison results

in table I clearly show the computational advantages of the

random sampling technique proposed here.

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results with simulation and a real wheelchair robot are pro-

vided in Sections IV and IV-A respectively. Finally, Section V

summarises the contribution of this paper.

II. BACKGROUND

In general terms, the sampling algorithms developed to

construct an approximate representation of the free space

currently available can be divided into two: single-query and

multiple-query approaches. Multiple-query approaches starts

with a pre-processing step that usually takes a large amount

of time but makes solving path planning problems in the

same environment faster. Probabilistic Roadmaps (PRMs) [6]

is an example of a multi-query approach that initially used

uniform sampling in constructing the path. This method was

problematic because the entire C-space will be sampled with

a density required by the most complex area of the environ-

ment, such as a narrow passage area. Nowadays, PRMs are

moving into a non-uniform methods for sampling such as the

Gaussian sampling method [10], and the bridge test to insure

that most of the conﬁgurations in C-space are actually close

to obstacles or inside a narrow passage, thus reducing the

unnecessary samples and decreasing the computational time.

Single-query methods were developed to avoid the large pre-

computational time that the multi-query methods take, and

they have been proved to be efﬁcient [15], [16]. Randomly-

exploring Random Trees (RRTs) [12], [18] are mainly based on

single-query methods. They have gained popularity from their

good performances, which has lead to a number of extensions

speciﬁcally targeting the solution to complicated geometrical

problems [17], such as the deterministic resolution-complete

alternatives that have been proposed to replace the random

sampling methods in [19].

In many cases, an optimal and not just a feasible path is

required. As a result of randomness, the paths generated by the

execution of the above planners are very often sub-optimal and

non-smooth. A two-phase approach was proposed in [8] to op-

timise paths generated in the special case where the ﬁrst-phase

path planned is made up of straight line segments connected

by way-points. Another two-phase planning algorithm based

on RRT was developed in [9]. This algorithm can compute

low cost paths given a desired cost function by a numerical

gradient descent algorithm that minimises the Hamiltonian of

the entire path.

The approach proposed here is based on a simple multi-

query one-phase planner that addresses the optimality and

smoothness weaknesses of probabilistic path planning algo-

rithms, a requirement for the general case of ﬁne motion

platforms, such as wheelchairs. The planner uses an a-priory

map of the environment to calculate an ofﬂine, minimal free

search space, where and additional smoothness cost function is

used to address the issues associated with smoothly navigating

a large robot in an environment with narrow passages and

obstacles.

III. PATH PLANNING ALGORITHM

The proposed algorithm starts by generating the search

space to containing information about the node position, the

(a) Before Expansion (b) After Expansion

Fig. 1. Largest robot dimension obstacle expansion method

connections to neighbouring nodes, a path smoothing penalty

which will be used later to ﬁne-tune the path during the on-line

planning, and a collision detection method. The on-line path

planning step consists of a path search using the A* algorithm

with a modiﬁed cost function to favour smooth ﬁne motions.

The result is an optimal and smooth path that can be quickly

generated in one step.

A. Generating the search space

The pre-processing step aims at minimising the on-line

computation by pre-generating a search space to contain all the

information that will be used during the on-line path planning,

while at the same time avoid generating an unnecessarily

complete and complex space. The steps used during the search

space creation can be deﬁned as follows:

Algorithm 1 C-space generation

Input: map, robot dimensions

1. Expand Obstacles.

2. Generate Regular Grid with low resolution.

3. Apply bridge test to add dense narrow passages.

4. Penalise nodes by adding a smoothing cost.

5. Connect nodes to form search space discretisation.

6. Eliminate those that cause collision.

Output: free search space.

1) Obstacle expansion: In this step obstacles are enlarged

with a radius Rto simplify the on-line collision detection by

reducing the number of points on the robots to be checked

for collision. It also reduces the number of nodes in the

search space thus increasing the on-line path planning perfor-

mance. The traditional approach [14] is based on expanding

the obstacles by a radius requivalent to the robots largest

dimension, hence planning as if the robot could navigate as a

point in the environment, as depicted in Figure 1. This over-

simpliﬁcation, however, is not suitable for the case of large

robots in constrained spaces, as expanding the obstacles along

narrow passages will effectively block the passage, as shown

in Figure 2.

A more suitable solution is proposed by ﬁnding the largest

possible expansion radius Rthat allows the robot to pass

through the narrowest path and then divide the area of the

robot into circles of that radius, as depicted in Figure 3. The

centre points of those circles will then be used to check for

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Fig. 2. Narrow passage blocked as a result of largest robot dimension obstacle

expansion

Fig. 3. The area of the robot is covered by circles of radius R, the centres

of these circles will be the points to be checked for collision

obstacle collision. The expansion radius Ris determined based

on the a-priory knowledge of the environment: suppose that

the narrowest passages is of width land the largest robot

dimension is rthen the largest expansion that allows the robot

to pass through can be determined by:

R=l−ε

2if l<2r

rotherwise (1)

where εis a minimal safety distance to make sure the platform

does not get uncomfortably close to the obstacles.

2) Regular grid discretisation: The C-space is then popu-

lated with nodes using a low resolution regular grid. This will

help in maintaining the connectivity of the graph by deﬁning a

minimum discretisation for the open spaces. The discretisation

density is adjusted to suit the environment, selecting as sparse

a grid as possible. Up to this stage the nodes hold only position

information.

3) Bridge test: Narrow passages in free space are small

regions critical in preserving the connectivity of a path during

the path planning process. Any attempt to sample the narrow

passages using a uniform distribution based on volume will

fail precisely because of their small volumes. The bridge test

[3] was introduced to boost the sampling density inside narrow

passages using only a simple test of the local geometry. Narrow

passage can be usually deﬁned as a space where the motion

of the robot is restricted in at least on direction and any small

changes in the robots conﬁguration in that direction may result

in a collision with obstacles. In these passages, robot motion is

limited to those directions perpendicular to the restricted ones.

A short line segment of length dcan sample randomly through

a point min the free space such that the end points of the line

segment lie in obstacles. This line segment is what we call a

bridge because it acts like a bridge across the narrow passage

with its endpoints in an occupied location and the point min

a free space. If we are able to build a bridge through point m,

then the bridge test is successful at this point and point mis

added to the search space.

Algorithm 2 Bridge Test

1. repeat

2. Pick a point pfrom the regular-grid map

3. If pis in an occupied location then

4. Pick a point pthat is ddistance away from p

5. If pis in an occupied location then

6. Let mbe the midpoint of ppline segment

7. If mis in a free location then

8. Insert minto the search space as a new node

Building short bridges is easier in narrow passages than

in free space and by favouring short bridges we increase the

chance of getting point in the narrow passages. The off-line

test increases the density of free-space sample points to our

search space where it matters most, in the narrow passages,

instead of the whole region. Figure 5 (further described later

in Section IV) shows the result of the bridge test on a map

with narrow passages.

4) Clearance (smoothness) penalty: Costs are added to the

nodes in C-space to indicate how far they are from an obstacle.

The cost Cpis a normalized cost that is inversely proportional

to this distance d, so that the closer the point is from an

obstacle the higher its cost, according to:

Cp=D−d

D(2)

where Dindicates the clearance distance beyond which the

node will be assigned a zero cost. This cost will be used during

the on-line path planning process to plan smoother paths in one

step, and no further smoothing step will be necessary after the

path is generated. The end results are paths which tend more

towards the middle of empty spaces and are within a safe

distance from the obstacles.

5) Node connections: In order to ﬁnd a path among the

resulting nodes, these need to be connected together. This is

done by establishing a link between each node and its neigh-

bouring nodes a certain distance away. The more neighbours

a node is linked to, the more discrete poses (position and

orientation) with be available during the search for a viable

path. However, there should be a compromise between the

Fig. 6. A case where the wheelchair robot has to go through two narrow

doors

TAB L E I

COMPARISON OF UNIFORM AND NON-UNIFORM C-SPACE GENERATION

Uniform Sampling Random Sampling

no. nodes 32364 15634

no. connections 691155 129479

time 1.8589 sec 0.3228 sec

A more challenging path planning problems where the

mobile robot had to manouvre to pass through two tight and

narrow passages is depicted in Figure 6. It can be seen how

the addition of search nodes where it really matters not only

makes ﬁnding a collision-free path feasible, but the additional

penalties also tend to direct the robot as far as possible from

obstacles along a smooth path.

A. Testing on a hardware platform

The real-time feasibility and smoothness of the approach

was also tested in a real mobile platform, a commercial

electric-powered wheelchair. The platform has two differen-

tially driven wheels at the rear, and two passive casters at

the front, and can travel at speeds of up to 15km/h. The

wheelchair, depicted in Figure 7, was instrumented with a

computer (attached behind the back rest), wheel encoders

and a laser range ﬁnder used for localisation. The functional

architecture of the system is described by the block diagram

of Figure 8.

The computing platform comprises of a 1 GHz Pentium

III processor with 256Mb RAM that communicates with the

two optical wheel encoders through the serial port. A laser

rangeﬁnder is located on the foot rest at the front of the

wheelchair and also communicates via a serial link with

the computer. The actual control of the wheelchair motion

takes place through an interface DAC box that is attached

to the joystick and simulates the standard command signals

that control the normal funcioning of the wheelchair as if

a user was controlling it, such as activating the motors,

increasing/decreasing the gears or sounding the horn amongst

others. The wheelchair measures 1.2x0.7m, by all accounts a

Fig. 7. Instrumented autonomous wheelchair platform

Fig. 8. Mobile platform navigational architecture

large robot when driving around a typical ofﬁce environment

with narrow passages, long corridors and cluttered static ob-

stacles. Tests were fully autonomous in that the wheelchair

was commanded to plan a path in the given map from a start

conﬁguration to a goal conﬁguration. A simple linear controller

based on displacement and orientation error was implemented

to traverse the path.

Figure 9 shows the result of navigating a similar path to that

depicted in Figure 5. Velocity of the wheelchair was constant

during the experiment at 0.2 m/sec. Localising the robot was

done through the Adaptive Monte Carlo Localization (AMCL)

algorithm [7] with the aid of the laser range-ﬁnder. A true

estimation of the location was provided every 2 seconds, and

dead-reckoning based on odometry and the kinematic vehicle

model was employed in between these updates to establish

the location of the vehicle. The goal was reached as shown in

Figure 9 shows how close the path was followed, achieving

the goal position within 3 cm and 5 degrees linear and angular

error. Similar results were obtained for other paths generated

Fig. 9. Result of navigating a path generated by the planner, where the thick

line represents the feedback position as estimated by the localizer, and the

thin line represents the actual planned path

in this environment.

V. C ONCLUSION AND FURTHER WORK

This paper has presented a new approach for generating

optimized smooth paths afor large platforms in constrained

spaces using a novel C-space creation method. A non-uniform

sampling technique has been proposed to efﬁciently target

the narrow passage problem, of particular relevance for such

large mobile platforms in cluttered environments. Results from

simulation and a real-time implementation in an automated

wheelchair have shown that the path planner was able to plan

one-stage smooth feasible paths, quickly and efﬁciently due to

the simplicity of the search space method prposed.

While these preliminary results have shown the feasibilty

of the motion planner to generate and navigate suitable paths

in what represents a challenging, if static, environment for

a large mobile platform, the next step is the introduction of

dynamic obstacles, which is by no means trivial. Further, the

current cost function gives preference to on-the-spot rotations,

circumventing non-holonomic constraints which could also be

taken into account. Also, efforts are being directed to apply

the advances presented here to the ﬁne motion planning and

control of a user-driven wheelchair, effectively allowing the

user think he/she is a better driver than he/she really is.

ACKNOWLEDGMENT

This work is supported by the Australian Research Council

(ARC) through its Centre of Excellence programme, and by

the New South Wales State Government. The ARC Centre of

Excellence for Autonomous Systems (CAS) is a partnership

between the University of Technology Sydney, the University

of Sydney and the University of New South Wales.

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