An efﬁcient strategy for robot navigation in
cluttered environments in the presence of dynamic
Jaime Valls Mir´
o, Tarek Taha, Dalong Wang, Gamini Dissanayake and Dikai Liu
ARC Centre of Excellence for Autonomous Systems (CAS)
Faculty of Engineering, University of Technology Sydney (UTS), NSW2007, Australia
Abstract— A novel method which combines an optimised global
path planner with real-time sensor-based collision avoidance
capabilities in order to avoid moving obstacles (e.g. people) in
a complex environment is presented. The strategy is based on
a time efﬁcient one step path planning algorithm for navigating
a large robotic platform in indoor environments. The planner,
which has been proved to compare favourably to currently
available path planning algorithms such as Randomly-exploring
Random Trees (RRTs) and Probabilistic Road Maps (PRMs)
in known static conditions, is enhanced here with a modiﬁed
Variable Speed Force Field (V S F 2) mechanism to accommodate
for dynamic changes of the environment. The basic concept
of the modiﬁed DV SF 2is to generate a continually changing
parameterised familiy of virtual force ﬁelds for the robot based
on characteristics such as location, travelling speed, heading and
dimension of all the objects present in the vicinity, static and
dynamic. The interactions among the repulsive forces associated
with the various obstacles provide a natural way for local collision
avoidance and situational awareness. This is harnessed here by
locally modifying the planned behaviour of the moving platform
in real time, whilst preserving as much as possible the optimised
nature of the global path. Furthermore, traversability of the
path is continually monitored by the global planner to trigger
a complete re-planning from the robot’s current location in the
case of major changes to the environment, most notably when the
path is completely blocked by an obstacle. Overall, a complete
solution to the navigational problem in partially known cluttered
environments is provided.
The problem of planning and tracking a path in a partially
known cluttered environment in the presence of other moving
objects is considered here. Classically, the simpler problem
of planning in static environments has been approached from
two perspectives, opposite to some extent, yet both reliant on
the use of advanced perception abilities to gather as much
information as possible about the environment:
•Use the sensorial data to build or modify a detailed
internal representation of this environment which the
robot would then use to (re)plan a feasible path from
source to the destination.
•Employ the measurements in a reactive obstacle avoid-
The former is the most generalised technique to address the
problem in highly structured environments as it follows the
intuitive sense-model-plan-act technique which more closely
resembles the human reasoning, and a vast number of solutions
can be found in the literature (see  for some examples).
However its performance in real scenarios is poor given the
unreliable nature of the perceived data and the high computa-
tional cost of modelling complex environments. Moreover any
changes in the robot surroundings require a reiteration of the
algorithm or the pre-computed path will almost certainly hit
obstacles, hence making it particularly unsuitable for dynamic
These perceived limitations have led to mobile robot navi-
gation modules where locally simple reactive behaviours are
in charge of computing the motion of the robot. Rather
than storing a detailed model of the world to compute a
geometric path free of collisions with the perceived obstacles,
the technique effectively uses the world as its own model,
introducing sensory information within the control loop. The
main drawback then becomes its locality in execution ,
as not all information is available to the robot’s sensors. For
this reason, while some form of reactive obstacle avoidance
behaviour becomes necessary (particularly in dynamic envi-
ronment), the use of a high-level world model and a global
planning strategy is also mandatory. This hybrid model has
emerged as the preferred motion planning architecture for
mobile platforms in use today.
In our previous work  we addressed the problem of
designing an efﬁcient near optimal global planner for mobile
platforms. The proposed solution was proved to be time
efﬁcient and feasible even in the case of large robots in narrow
passages, and compared favourably to currently available static
path planning algorithms such as RRTs and PRMs. However,
the uncertainties the system was capable of dealing with were
limited to those a simple linear controller could overcome in
bringing the robot back to the pre-planned path. The absence
of an interactive response to changes in the environment meant
the solution was limited to known static environments. In
the work presented here these shortcomings are overcame by
introducing a novel reactive planner in the loop in line with
the hybrid approach scenario described.
The main contribution of this paper lies with the framework
proposed to ensure safe and optimal navigation of a robot in
uncertain dynamically changing scenarios. Given a partially
known model of the environment, a higher-level planner 
is employed for describing an optimised path from source to
destination, and also for constantly monitoring the traversibil-
ity of the waypoints to trigger a global re-planning when
the feasible path gets obstructed. An innovative strategy is
then presented to handle underlying local navigation issues
in between waypoints. The methodology, framed within the
context of a force ﬁeld approach recently proposed in the
literature for multi-robot path planning and collaboration ,
is suitably modiﬁed here to handle the behaviour of the robot
at a local scale in the presence not only of static changes
and uncertain localisation within the environment, but also
of moving objects in the vicinity. In the approach, a virtual
force ﬁeld is constructed around the robot based on the
current characteristics from the moving platform itself such
as travelling speed, dimension and location, combined with
the status of the surrounding dynamic and static obstacles
as given by the sensorial information. It is the interaction of
all the attractive and repulsive forces at play what drives the
robot towards its local goal in an efﬁcient and natural manner.
This is demonstrated with the simulation of an autonomous
wheelchair operating in a challenging ofﬁce-like scenario with
dynamic obstacles moving nearby.
The remainder of this manuscript is organised as follows:
latest proposals to the path planing and obstacle avoidance
problem and where our approach represents an improvement is
analysed in Section II. The methodology used for the creation
of the search space and the actual path ﬁnding is summarised
in Section III, with Section IV focusing on the proposed force
ﬁeld reactive planner. Detailed simulation results are given in
Section V. Finally, Section VI summarises the contributions
of this paper and future work.
II. PATH PLANNING AND OBSTACLE AVOIDANCE
A. Path Planning
Motion planning is characterised by the ability to compute
a collision-free path from an initial pose to a goal position in
between static obstacles, or by maintaining a set of constraints
in the state of the world such as following a target or exploring
unknown environments. Motion planning has been extensively
studied and the reader is referred to  for a thorough
review. Most of the current approaches are based on the con-
cept of conﬁguration space (C-space) introduced by Lozano-
erez  and Wesley  in which robots are regarded as
a single point in a high dimensional space equivalent to the
degrees of freedom of the robot. As the obstacles are generally
expanded in an over-simplistic manner by the length of the
larger robot dimension, this approach very often prevents
larger robots in cluttered environment from ever reaching a
solution, even when it exists .
The exact construction of the C-space is a computationally
expensive solution  and sampling-based techniques, in
which a random set of points are used to represent the C-space,
have been develop which provide a faster practical solution by
sacriﬁcing completeness , . Traditionally, sampling-
based algorithms are based on uniform sampling which con-
siders the whole environment as uniformly complex and thus
the overall sampling density will be equivalent to that needed
by the most complex region, reaching its worst case scenario
when narrow passage areas exist in the environment . Non-
uniform methods such as the Gaussian sampling strategy 
and the bridge test  have been proposed to ensure that
most of the conﬁguration space is actually close to obstacles
or inside a narrow passage, thus reducing unnecessary samples
and decreasing the computational time.
Sampling algorithms are generally divided into two based on
the complexity of the pre-processing step heuristics which set
up the search space: multi-query and single-query approaches.
The former starts with a step that usually takes a large amount
of time but makes solving path planning problems in the same
environment faster. Probabilistic Road Maps (PRMs) 
is an example of a multi-query approach that initially used
uniform sampling in constructing the path, although nowadays
PRMs are moving into non-uniform sampling methods .
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 . Randomly-
exploring Random Trees (RRTs) , , mainly based
on single-query methods, have gained popularity from their
good performances. This has lead to a number of extensions
speciﬁcally targeted to the solution of complicated geometrical
problems , such as the deterministic resolution-complete
alternatives that have been proposed to replace the random
sampling methods in .
In many cases, an optimal and not just a feasible path is
required. The random nature of the above planners means the
paths generated are very often sub-optimal and non-smooth,
not particularly suitable for realistic robot traversal. A two-
phase approach was proposed in  to optimise paths in the
special case where the ﬁrst-phase generated paths are made
up of straight line segments connected by way-points. Another
two-phase planning algorithm based on RRT was developed
in  where low cost paths are computed by a numerical
gradient descent algorithm that minimises the Hamiltonian
of the entire path. In this work, a hybrid time-efﬁcient path
planning algorithm developed by the authors which has proved
to compare favourably to PRMs and RRTs  has been
employed. The strategy, based on a non-uniform multi-query
planner, uses an a-priory static map of the environment to
calculate an ofﬂine, minimalistic free search space where com-
putational resources are directed towards the narrow passages.
The algorithm takes further advantage of techniques like the
bridge test and an optimised obstacle expansion method to
further reduce the number of samples and the points to be
check for obstacle collision. The optimality and smoothness
weaknesses of probabilistic path planners is addressed by the
addition of a smooth cost function to the search space. A
modiﬁed A* search is then implemented to ﬁnd suitable paths
on this space. The result is a time-efﬁcient path planner with
smooth and cost optimal paths.
B. Obstacle Avoidance
Local obstacle avoidance methods focus on changing the
robot’s trajectory based on its sensors data during robot
motion. The ”bug” algorithm , which proposes to cir-
cumnavigate the obstacles by following the contour of each
obstacle in the robot’s way is perhaps the simplest obstacle
avoidance algorithm, where no control, kinematic or dynamic
constraints are considered. Techniques such as potential ﬁeld
methods  are particularly attractive too as their simple
conception can be used for on-line purposes to drive the robot
among static obstacles towards the target. Here the robot is
treated as a point under the inﬂuence of an artiﬁcial potential
ﬁeld. The basic idea behind all potential ﬁeld approaches
is that the robot is attracted toward the goal, while being
repulsed by the sensed obstacles. Although the approach does
not take into account robot kinematics, other strategies have
been proposed to transform the three-dimensional obstacle
avoidance problem with shape and kinematics constraints into
the simpler planning scenario of a point moving in a two-
dimensional space without kinematic restrictions .
However, traditionally the problem is solved in the control
space by computing a set of collision-free admissible motions,
followed by a selection based on some form of optimisation
and convergence towards the target. This is the case of
the curvature velocity method (CVM) , which takes the
actual kinematics constrains and some dynamic constrains
into account. The drawback of this method resides in the
circular simpliﬁcations attributed to the shape of the obstacles,
and the existence of local minima. Other techniques which
also take into account admissible controls and robot shape
constraints include the dynamic window obstacle avoidance
method (DWA)  and the global dynamic window approach
(GDWA)  variation.
The family of vector ﬁeld histogram (VFH)  techniques
also take into consideration some form of kinematic/dynamic
constraints and is a preferred choice in mobile robot appli-
cations for its speed and results. The algorithm looks for
gaps between the obstacles in front of the robot and builds
a local map based on the concept of certainty grid  from
recent sensor range readings. A variation of the original, the
VFH+ , ﬁrst comes up with a simpliﬁed model of the
moving robot’s possible trajectories based on its kinematics
limitations. Then obstacles which block the robot’s allowable
trajectories are properly taken into account in a masked polar
histogram. VFH* introduced the A* search into the direction
determination and has been proved to obtain better solutions
than VFH+ in certain cases .
A method which is particularly relevant to the work pre-
sented here is the elastic band method proposed in . This
technique tries to combine the global path planning with real-
time sensor-based collision avoidance. A pre-planned global
path is deformed in real time to keep a robot away from
obstacles during its movement, while the internal contraction
forces will bring the robot back to its original path when the
obstacle is out of the sensor range. The method takes also into
account the actual shape of the robot and restricts the search
space by the concept of a ”bubble”. A bubble is deﬁned as
the maximum local subset of the free space around a given
conﬁguration of the robot which can be safely travelled in
any direction without collisions. Given such bubbles, a band
or string of bubbles can be used along the trajectory from the
robot’s initial position to its goal position to show the robots
expected free space along the pre-planned path.
The obstacle avoidance techniques just mentioned and oth-
ers variations which follow similar concepts have been proved
to be effective in the presence of static obstacles in the
environment. However, one aspect they all have in common
is that they are not directly applicable to deal with dynamic
obstacles, since characteristics from the moving objects such
as travelling speed, size, etc. are not built into the algorithms.
That is not to say some of them will not be able to deal
with a certain degree of dynamism in the environment, but it
is not designed in their methodology to do it in an efﬁcient
manner. The DV S F 2obstacle avoidance technique proposed
here is designed around these premises and performs well in
partially known and continuously changing environments. Its
basic principle is to generate a repelling force ﬁeld for the
robot based on its own kinematic and dynamic status and those
of the moving objects, as well as the the static obstacles to
generate a combined force that drives the robot towards the
III. THE OPTIMISED GLOBAL PLANNER
In this section an overview of the proposed path planner
algorithm is given. Further details can be obtained from .
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.
The steps used during the search space creation can be deﬁned
Algorithm 1 Search-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) Collision Detection: 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. This is done 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 Fig. 1. The centre points of those circles
Fig. 1. 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.
will then be used to check for obstacle collision. The expansion
radius Ris determined based on the a-priory knowledge of the
environment: suppose that the narrowest passages is of width l
and the largest robot dimension is rthen the largest expansion
that allows the robot to pass through can be determined by:
2if l < 2r
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
3) Bridge Test: The bridge test  was introduced to
boost the sampling density inside narrow passages using only
a simple test of the local geometry. 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
4) Clearance (Smoothness) Penalty: To insure that the
paths generated are directed to the middle of the empty space
not adjacent to the obstacles, we introduced a cost added to
the the nodes in the search space indicating 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:
Algorithm 2 Bridge test
2. Pick a point pfrom the regular-grid map
3. If pis in an occupied location then
4. Pick a point p′that is ddistance away from p
5. If p′is in an occupied location then
6. Let mbe the midpoint of pp′line segment
7. If mis in a free location then
8. Insert minto the search space as a new node
where Kdindicates 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
5) Node Connections: In order to ﬁnd a path among the
resulting nodes, these need to be connected together in a tree
structure. This is done by establishing a link between each
node and its neighbouring 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.
6) Connections Reduction: In a ﬁnal step we eliminate
those connections that cause a collision of the platform with
the obstacles. The connections between nodes determines the
possible orientations of the robot should it follow that path.
The centre 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.
B. On-line Path Planning
In the algorithm proposed here, we use the well know A*
algorithm where our 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 ∆θ x where x
is the length of the axis of the rear wheels, the sum of the
clearance penalties Cppreviously computed ofﬂine - which
is directly proportional to the distance ∆d, the number of
reversals (backward motion) in the path nrev and the heuristic
function hrepresenting the distance to goal at each step. The
cost function, deﬁned as follows:
J(d) = X∆d+X∆θ x +X∆d Cp+Xnrev +h(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. THE VIRTUAL FORCE FIELD FOR LOCAL
This section describes the modiﬁed V SF 2method for local
re-planning in the presence of static and dynamic obstacles,
Fig. 2. The repulsive virtual force ﬁeld generated by an obstacle on the
DV SF 2. For more details on the V S F 2for multi-robot
motion planning the reader may refer to .
A. Deﬁnition of the Force Field
A force ﬁeld is deﬁned as a virtual repulsive force in
the vicinity of a robot, whose magnitude and orientation
varies constantly with the robot’s status as it travels along
the workspace towards the goal. Intuitively, it is a force
that increases as the sensed distance to any obstacles in the
environment decreases, hence keeping the robot from hitting
To introduce the concept of the virtual force ﬁeld is im-
portant to understand how the interacting forces from obsta-
cles and robot are calculated. Assuming a rectangular-shape
differential-drive platform like the automated wheelchair robot
considered here, restricted to move on a ﬂat surface, the
contours of the force ﬁelds at various distances Dare geomet-
rically represented by conic sections of different eccentricities,
as depicted in Fig. 2. The robot coordinate system, at its centre
of rotation, coincides with the conic section focus, and the
robot’s Xraxis lies along the conic section’s major axis. It
is shown how Dmax describes the maximum distance where
the ﬁeld is felt, whilst Dmin is the distance at which this
robot has maximum repulsive force. Or, in other words, Dmax
represents how far the robot can inﬂuence its vicinity, and
Dmin preserves a safe area around the robot onto which no
other objects should ever be present. These relationships can
be mathematically described in the robot reference system
depicted in Fig. 3. Let Rr be the radius, from the robot’s
origin, of the maximum circle embedding the robot, θrthe
robot orientation in the global coordinates, θthe orientation of
the obstacle relative to the robot, and vrthe linear component
of the robot speed (vmax being its maximum value). Then:
Dmax = (KrRr)Er
Dmin =Kdmin Dmax (6)
Fig. 3. Reference parameters that deﬁne the robot’s virtual force ﬁeld.
Kvis the eccentricity factor required to limit the speed
ratio Erso that when vr=vmax the resulting conic is an
ellipse. This is required to guarantee the effect of the ﬁeld is
felt in a limited, closed area around the robot. A parabolic or
hyperbolic open ended ﬁeld would not allow for the proper
detection of the obstacles around the robot as it moves about.
The factor Rrallows us to take the size of the robot in the
calculations of the ﬁeld, so that bigger platforms generate
larger ﬁelds, whilst the positive multiplier Krrepresents an
extra degree of control of the inﬂuence that the environment
has in the resulting ﬁeld by permitting larger virtual ﬁelds
when the area is a-priory known to be fairly clear of obstacles.
Dmin is a percentage of Dmax, i.e, 0< Kdmin <1. The
choice of Kdmin denotes to some extent the environment’s
inﬂuence on the force, as it heavily inﬂuences how close
the robot can get to obstacles. For a large robot such as a
wheelchair operating through narrow doors this needs to be
fairly small, or the robot will get stuck.
1) Repulsive Force: With the above deﬁnitions in mind, the
repulsive force generated by a robot at a distance Dfrom its
boundary is deﬁned by:
0D > Dmax
Dmax−Dmin Dmin ≤D < Dmax
where Kfis a positive constant which determines the mag-
nitude of the repulsive force. As distance Dchanges from
Dmin to Dmax the magnitude of the repulsive force changes
gradually from Kfto 0. Equation (7) can be easily transformed
to emphasise the concept of the contour of the force ﬁeld as
seen in Fig. 2 by deﬁning
so that (7) becomes:
0ρ > 1
1−ρ0ρ0≤ρ < 1
Now when ρchanges from ρ0to 1, the magnitude of
repulsive force changes from Kfto 0. With this mapping
Eq. (6) becomes:
Dmin =ρ0Dmax (10)
Given the manifold of repulsive force ﬁelds that accompany
the robot in its motion, when an obstacle is sensed in the
vicinity, the interaction point where the maximum repulsive
force is felt is selected as the repelling contour force for the
2) Attractive Force: At any given time a goal is selected
as the furthest visible point provided by the sensor along the
optimised pre-planned global path. A virtual attractive force
Fattr is associated with this local target to attract the robot
from its current location towards the goal. The attractive force
is presumed exerted from the centre of rotation of the robot
and is calculated as a positive value set to be larger than the
sum of all repulsive forces from the obstacles, so that the robot
is guaranteed to always being pulled in the broad direction of
B. The Combined Forces
The resulting forces exhorted on the robot can then be
Frep total (11)
where the reaction repulsive force is the sum of the ﬁelds
from each of the nobstacles - static and dynamic - observed
in the local are, as given by
Frep total =
C. The D V S F 2Controller
The motion of a wheelchair-like differential robot in a two-
dimensional surface is constrained by the well-known non-
−˙xsin θ+ ˙ycos θ= 0 (13)
whose effect is to reduce the dimension of the location and
orientation conﬁguration space q= (x, y, θ)to a kinematic
model whose instantaneous velocity lateral to the heading
has to be zero. This is normally expressed in terms of
the translational movement vr, and the rotation movement
about its centre of mass ωr, which are also the controls
of the wheelchair robot. Hence, given the interacting forces
expressed by Eq. (11), the following motion controls are
1 + max(|~
Ftotal, ωr)is a normalising function of the angular
error difference between the desired direction along the resul-
tant force 6~
Ftotal and the robot’s current orientation, while
Eq. (14) guarantees that the robot’s speed will be sensibly
inﬂuenced by the obstacles’ repulsive forces.
V. EXPERIMENTAL RESULTS
The results of simulating the proposed algorithm in an auto-
mated wheelchair platform are presented next. The mechanical
platform measures 1.2m×0.7m, by all accounts a large
robot when made to manoeuvre in a challenging ofﬁce-like
environment with narrow passages, doors, long corridors and
cluttered static obstacles. The wheelchair has two differentially
driven wheels at the rear and two passive casters at the front
and can travel at speeds of up to 15km/h. The planner was
commanded to ﬁnd an optimal path in a given map, rather
noisy as it has been obtained via ICP scan-matching of data
collected by driving the real platform around the area. Given
a start and goal conﬁgurations the planner ﬁnds the shortest
collision-free path shown in Fig. 4(a). Note the smoothness
and how the planner tends to direct the robot as far as possible
from obstacles and along the middle of the empty spaces,
making the path not only feasible and kinematically “gentle”
on the platform, but also maximising clearances with the
obstacles known at this stage along the minimal distance path.
Fig. 4(b) depicts the scenario when a static obstacle (red
square box) is placed in the robot surroundings as it is
navigating along the given path. It can be seen how the active
DV F F 2is capable of avoiding the obstacle, generating the
tracking trajectory shown in blue. The presence of a moving
obstacle in the narrow corridor seen in Fig. 4(c) also makes
the controller take evasive action. The close proximity of the
robot and the dynamic obstacle has as a result slow motions,
the robot picking up speed once the obstacle has been cleared.
This is also the case when the platform crosses narrow spaces
such as doors, as forces sensed from the environment are
exerted on the platform in opposed directions, effectively
resulting in reduced linear speeds. For the simulations pre-
sented here the moving obstacle has been made to follow
a predetermined path, tracked by a constant speed linear
controller, with the objective to simulate the presence of a
person moving about in the vicinity.
In the ﬁnal scenario considered, the path the robot is made
to follow is completely blocked by the presence of the static
obstacle. The planner is capable of discerning this situation
which triggers a complete re-planning. ICP is used to register
the changes in the virtual map and the search space is modiﬁed
accordingly, removing the blocked nodes and ﬁnding a new
path from the robot current’s location to the goal 1. An
example is displayed in Fig. 4(d).
1The whole re-planning process is fast, around 300ms in a modern PC, but
the robot is nevertheless stopped for some time while it takes place for security
reasons, with the view of implementing the strategy on the real platform.
(a) Initial conﬁguration, clear of obstacles. (b) Reacting to a new static obstacle (red) in the scene.
(c) Reacting to the presence of a dynamic obstacle (orange) in the scene. (d) The path is fully blocked and a major re-planning is carried out.
Fig. 4. A case study of the robot navigation strategy in action in the presence of static and dynamic obstacles.
An intrinsic drawback of the proposed methodology is due
to the reactive speed changes as dictated by the DV S F 2
controller. In can be observed how when traversing narrow
passages such as doors, the repulsive force ﬁeld felt by the
robot produces slightly oscillating angular motions. This is
because as the robot is made to closely approach the Dmin
discomfort zone, the strongest of repulsive forces are at play.
The zealous safety-oriented proposed controls dictate very
slow linear speeds for this scenario, which combine with the
fast nature of the opposing repulsive forces and manifest in the
angular controls oscillating behaviour. While this known issue
is dampened on the real platform, a low-pass ﬁlter is never-
theless necessary to smooth out this undesirable behaviour.
The approach is currently being implemented on the real
wheelchair platform , where more engineering work is under-
way to provide it with better sensing capabilities to be able to
fully demonstrate the concept.
VI. CONCLUSIONS AND FUTURE WORKS
A local obstacle avoidance controller integrated within an
optimised path planner has been proposed to counteract the
effect of uncertainties arising from planning in an ever chang-
ing world. Based on perceptive data, and the kinematic status
of robot and surroundings, a varying family of virtual force
ﬁelds are generated around the moving platform in response
to objects in the environment. The effect of this repulsive
force (null in the absence of obstacles) is to maximise the
safe motion of the robot towards the local waypoints provided
by the planner, “shielding” the platform in an optimal manner
and preventing collisions with the objects in the local area,
static and dynamic.
An array of challenging simulated scenarios have been pre-
sented to demonstrate the good results of the proposed reactive
behaviour in cluttered environments. This was made even more
acute given the dimensions and mobility of the robot - an
automated wheelchair - with respect to its surroundings.
Work is currently underway to implement the proposal in
the real wheelchair platform. A mechanism to segmenting out
the moving obstacle from its surroundings is necessary to fully
demonstrate the approach, and a moving object detection and
tracking strategy  is being developed.
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.
 T. Taha, J. Valls Mir´
o and Gamini Dissanayake. Sampling Based Time
Efﬁcient Path Planning Algorithm for Mobile Platforms, in International
Conference on Man-Machine Systems, Sep 2006. (to be published)
 T. Taha, J. Valls Mir´
o and D. Liu. An Efﬁcient Path Planner for Large
Mobile Platforms in Cluttered Environments, in IEEE International
Conference on Robotics, Automation and Mechatronics, 225-230, Jun
 D. Wang, D. Liu and G. Dissanayake. A Variable Speed Force Field
Method for Multi-Robot Collaboration, in IEEE/RSJ International Con-
ference on Intelligent Robots and Systems, Beijing, China, Oct 2006. (to
 J. C. Latombe. Motion Planning : A Journey of Robots, Molecules,
Digital Actors, and Other Artifacts, International Journal of Robotics
Research, vol.18, no.11, 1119-1128, 1999.
 J.H. Reif. Complexity of the Mover’s Problem and Generalizations, in
Proc. of IEEE Symposium on Foundations of Computer Science, New
York, 421-427, 1979.
 J. Barraquand and J.C. Latombe. Robot Motion Planning: A Distributed
Representation Approach, The International Journal of Robotics Re-
search 10, no.6, 628-649, Dec. 1991.
 W. Burgard, A.B. Cremers, D. Fox, D. Hahnel, G. Lakemeyer, D. Schulz,
W. Steiner and S. Thrun. The Interactive Museum Tourguide Robot,
In Proc.of the Fifteenth National Conference on Artiﬁcial Intelligence,
Madison, Wi, 1998.
 Chang, H. and T.-Y. Lai. Assembly Maintainability Study with Motion
Planning, in Proc. of IEEE International Conference on Robotics and
Automation, Los Alamitos, CA, 1012-1019, 1995.
 D. Brutlag, M.S. Apaydin, C. Guestrin, D. Hsu, C. Varma, A. Singh
and J.-C. Latombe. Using Robotics to Fold Proteins and Dock Ligands,
Bioinformatics, 18:S74-S83, 2002.
 T. Lozano-P´
erez. Spatial Planning: a Conﬁguration Space Approach,
IEEE Transactions on Computers, vol. C-32, 108-120, IEEE Press, 1983.
 T. Lozano-P´
erez and M. Wesley. An Algorithm for Planning Collision-
free Paths among Polyhedral Obstacles, Communications of the ACM,
vol.22, no.10, 560-570, Oct 1979.
 Y. K. Hwang and N. Ahuja. Gross Motion Planning - A Survey, ACM
Computing Surveys, 24, no.3, 219-291, Sep 1992.
 D. Hsu, L. E. Kavaki, J. C. Latombe, R. Motwani and S. Sorkin. On
ﬁnding narrow passages with probabilistic roadmap planners, In Proc.
of Workshop on the Algorithm Foundations of Robotics, 141-154, A K
 D. Hsu, T. Jiang, J. Reif and Z. Sun. The bridge test for sampling
narrow passages with probabilistic roadmap planners, In Proc. of IEEE
International Conference on Robotics and Automation, 4420-4426, 2003.
 L. E. Kavraki, P. Svestka, J. C Latombe and M. H. Overmars. Proba-
bilistic Roadmaps for Path Planning in High-Dimensional Conﬁguration
Spaces. IEEE Trans. on Robotics and Automation, vol.12, no.4, 566-580,
 V. Boor, M. H. Overmars and A. F. van Der Stappen. The Gaussian
Sampling Strategy for Probabilistic Roadmap Planners, in Proc. of IEEE
International Conference on Robotics and Automation, 1018-1023, 1999.
 G. Sanchez and J. C. Latombe. A Single-query Bi-directional Proba-
bilistic Roadmap Planner with Lazy Collision Checking, in Int. Symp.
Robotics Research, 2001.
 S. M. LaValle. Rapidly-exploring Random Trees: a New Tool for Path
Planning, TR 98-11, Computer Science Dept., Iowa State University, Oct
 P. Cheng and S.M. La Valle . Resolution Complete Rapidly Exploring
Random Trees, in Proc. IEEE Intl. Conf. on Robotics and Automation,
 P. Choudhury and K. Lynch. Trajectory Planning for Second-order Under
Actuated Mechanical Systems in Presence of Obstacles, in Proc. of the
Workshop on Algorithmic Foundation of Robotics, 2002.
 J. Kim and J.P. Ostrowski. Motion Planning of Aerial Robot Using
Rapidly-Exploring Random Trees with Dynamic Constraints, in IEEE
Int. Conf. Robot. & Autom., 2200-2205, 2003.
 J. M. Philips, N. Bedrossian and L. E. Kavraki. Guided Expansive
Spaces Trees: a Search Strategy for Motion and Cost-constrained State
Spaces, in Proc. IEEE Int. Conf. Robot. & Autom. , 3968-3973, 2004.
 S. G. Vougiouksa. Optimization of Robot Paths Computed by Ran-
domised Planners, in Proc. of Int. Conf. on Robot. & Autom., 2160-2165,
 J. Barraquand, L. E. Kavraki , J. C. Latombe, T. Y. Li, R. Motwani
and P. A. Raghavan. Random Sampling Scheme for Path Planning,
International Journal of Robotics Research, vol.16 no.6, 759-774, 1997.
 S. M. La Valle. http://msl.cs.uiuc.edu/msl
 S. M. LaValle and J. J. Kuffner. Randomized Kinodynamic Planning, in
Proc. IEEE Int’l Conf. on Robotics and Automation, 473-479, 1999.
 V. J. Lumelsky and T. Skewis. Incorporating Range Sensing in the
Robot Navigation Function, IEEE Transactions on Systems, Man and
Cybernetics, vol.20, 1058-1069, 1990.
 O. Khatib. Real-time Obstacle Avoidance for Manipulators and Mobile
Robots, Int. Journal of Robotics Research, vol.5, 90-98, 1986.
 J. Borenstein and Y. Koren. Real-time Obstacle Avoidance for Fast
Mobile Robots in Cluttered Environments, in Proc. of IEEE International
Conference on Robotics and Automation, vol.1, 572-577, 1990.
 H. Moravec and A. Elfes. High Resolution Maps from Wide Angle
Sonar, in Proc. of IEEE International Conference on Robotics and
Automation, vol.2, 116-121, 1985.
 I. Ulrich and J. Borenstein. VFH+: Reliable Obstacle Avoidance for Fast
Mobile Robots, in Proc. of IEEE International Conference on Robotics
and Automation, vol.2, 1572-1577, 1998.
 I. Ulrich and J. Borenstein. VFH*: Local Obstacle Avoidance with
Look-Ahead Veriﬁcation, in Proc of IEEE International Conference on
Robotics and Automation, vol.3, 2505-2511, 2000.
 S. Quinlan and O. Khatib. Elastic Bands: Connecting Path Planning and
Control, in Proc. of IEEE International Conference on Robotics and
Automation, vol.2, 802-807, 1993.
 R. Simmons. The Curvature-Velocity Method for Local Obstacle Avoid-
ance, in Proc. of IEEE International Conference on Robotics and
Automation, vol.4, 3375-3382, 1996.
 D. Fox, W. Burgard, and S. Thrun. The Dynamic Window Approach
to Collision Avoidance, IEEE Robotics & Automation Magazine, vol. 4,
 O. Brock and O. Khatib. High-speed Navigation Using the Global
Dynamic Window Approach, in Proc. of IEEE International Conference
on Robotics and Automation, vol.1, 341-346, 1999.
 J. Minguez, L. Montano and J. Santos-Victor. Abstracting Vehicle
Shape and Kinematic Constraints from Obstacle Avoidance Methods,
Autonomous Robots, 2005.
 C. Wang, C. Thorpe and A. Suppe. LADAR-based Detection and
Tracking of Moving Objects from a Ground Vehicle at High Speeds,
in Proc. of IEEE Intelligent Vehicles Symposium, 416-421, Jun 2003.