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An efficient strategy for robot navigation in cluttered environments in the presence of dynamic obstacles

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Abstract and Figures

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 SF^2) mechanism to accommodate for dynamic changes of the environment. The basic concept of the modified DV SF^2 is 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.
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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}
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.
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
inak-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
1–4244–0025–2/06/$20.00 c
2006 IEEE RAM 2006
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.
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
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
Fig. 2. Narrow passage blocked as a result of largest robot dimension obstacle
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:
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
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:
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
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:
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.
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.
Fig. 6. A case where the wheelchair robot has to go through two narrow
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.
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.
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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The PSO based-Canonical Force Field (PSO-CF2) method is a novel approach of mobile robot path planning with collision avoidance. The choice of CF2 parameters is however vital to its performance. In this paper, we propose the multi-objective Particle Swarm Optimization Canonical Force Field (PSO-CF2) technique to search for the best combination of these parameters that minimizes the robot path length and maximizes the safe distance between the robot and the obstacles. Simulations are carried out in various environments (one obstacle, two obstacles and multi-obstacles). The results of these simulations show the feasibility of this Mobile Robot path planning approch.
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PSO-DVSF2 and PSO-CF2 are two PSO optimized F2 based motion planning approaches that we have previously proposed for mobile robots to achieve fixed destinations. The difference is that the robot travels with a fixed speed in the case of PSO-CF2 and with a variable speed in the case of PSO-DVSF2. In this paper, the capabilities of both approaches are enhanced in the sense of being able to track and reach a moving target whatever the environment is static or dynamic. In each step of robot’s movement, PSO-DVSF2 and PSO-CF2 receive the new position of the destination to update the linear and the angular speeds of the robot. PSO adjusts the F2 parameters to select the shortest and the safest path to the moving goal. Simulation results prove the ability of PSO-DVSF2 and PSO-CF2 to achieve moving targets regardless of the complexity of the environment whether it is static or dynamic.
In mobile robot research domain and especially in its path planning sub-domain, the optimization tools the most used are PSO (Particle Swarm Optimization) and GA (Genetic Algorithms). In fact, mobile robot path planning is a multi-objective optimization problem where at least these objectives are considered: the shortest and the safest path to the goal. Sometimes other objectives are added like travel duration. The subject of this paper is a comparison investigation concerning the efficiency of PSO and GA in mobile robot path planning optimization. We start with a comparison of evolutionary performances of PSO and GA. Then, we apply PSO and GA in the optimization of parameters of DVSF\(^{2}\) (Dynamic Variable Speed Force Field) path planning approach. Different environments of different types, statics and dynamics are considered in these simulations to decide which is better for mobile robot path planning optimization: PSO or GA.
Conference Paper
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This paper presents a new algorithm for mobile robot localization, called Monte Carlo Localization (MCL). MCL is a version of Markov localization, a family of probabilistic approaches that have recently been applied with great practical success. However, previous approaches were either computationally cumbersome (such as grid-based approaches that represent the state space by high-resolution 3D grids), or had to resort to extremely coarse-grained resolutions. Our approach is computationally efficient while retaining the ability to represent (almost) arbitrary distributions. MCL applies sampling-based methods for approximating probability distributions, in a way that places computation "where needed." The number of samples is adapted on-line, thereby invoking large sample sets only when necessary. Empirical results illustrate that MCL yields improved accuracy while requiring an order of magnitude less computation when compared to previous approaches. It is also much easier to implement.
Conference Paper
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This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: (1) single- query -i.e., it does not pre-compute a roadmap, but uses the two input query configurations to explore as little space as possible; (2) bi-directional i.e., it searches the robot's free space by concurrently building a roadmap made of two trees rooted at the query configurations - and (3) applies a sys- tematic lazy collision-checking strategy -i.e., it postpones collision tests along connections in the roadmap until they are absolutely needed. Several observations motivated this collision-checking strategy: (1) PRM planners spend more than 90% of their time checking collision; (2) most connec- tions in a PRM are not on the final path; (3) the collision test for a connection is the most expensive when there is no collision; and (4) the probability that a short connection is collision-free is large. The strengths of single-query and bi- directional sampling techniques, and those of lazy collision checking reinforce each other. This combination reduces planning time by large factors, making it possible to han- dle more difficult planning problems, including multi-robot problems in geometrically complex environments.
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A hierarchical representation for configuration space is presented, along with an algorithm for searching that space for collision-free paths. The detail of the algorithm are presented for polygonal obstacles and a moving object with two translational and one rotational degrees of freedom.
Conference Paper
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Motion planning for systems with constraints on controls or the need for relatively straight paths for real-time actions presents challenges for modern planners. This paper presents an approach which addresses these types of systems by building on existing motion planning approaches. Guided Expansive Spaces Trees are introduced to search for a low cost and relatively straight path in a space with motion constraints. Path Gradient Descent, which builds on the idea of Elastic Strips, finds the locally optimal path for an existing path. These techniques are tested on simulations of rendezvous and docking of the space shuttle to the International Space Station and of a 4-foot fan-controlled blimp in a factory setting.
During the past three decades, motion planning has emerged as a crucial and productive research area in robotics. In the mid-1980s, the most advanced planners were barely able to compute collision-free paths for objects crawling in planar workspaces. Today, planners efficiently deal with robots with many degrees of freedom in complex environments. Techniques also exist to generate quasi-optimal trajectories, coordinate multiple robots, deal with dynamic and kinematic constraints, and handle dynamic environments. This paper describes some of these achievements, presents new problems that have recently emerged, discusses applications likely to motivate future research, and finally gives expectations for the coming years. It stresses the fact that nonrobotics applications (e.g., graphic animation, surgical planning, computational biology) are growing in importance and are likely to shape future motion-planning research more than robotics itself.
Our paper on the use of heuristic information in graph searching defined a path-finding algorithm, A*, and proved that it had two important properties. In the notation of the paper, we proved that if the heuristic function ñ (n) is a lower bound on the true minimal cost from node n to a goal node, then A* is admissible; i.e., it would find a minimal cost path if any path to a goal node existed. Further, we proved that if the heuristic function also satisfied something called the consistency assumption, then A* was optimal; i.e., it expanded no more nodes than any other admissible algorithm A no more informed than A*. These results were summarized in a book by one of us.
Conference Paper
Maintainability is an important issue in design where the accessibility of certain parts is determined for routine maintenance. In the past its study has been largely manual and labor intensive. Either by using physical mockup or computer animation with CAD models of a design, the task relies on a human to provide an access path for the part. In this paper, the authors present an automated approach to replace this manual process. By applying results from and developing extensions to research in motion planning and other fields, the authors demonstrate that an automated maintainability study system is feasible. The authors describe general extensions needed to adapt robotic motion planning techniques in maintainability studies. The authors show results from applying such a system to two classes of industrial application problems
Conference Paper
Randomized path planners have been successfully used to compute feasible paths for difficult planning problems. Such paths are typically computed without taking into account any optimality criteria and may contain many “jagged” segments because of the randomness involved in their generation. This paper presents a two-phase path planning algorithm, which uses a randomized planner to compute low-cost paths, and gradient descent to locally optimize these paths by minimizing a Hamiltonian function. The algorithm is tested on motion planning for a non-holonomic car-like robot. The results indicate that the two-phase approach is practical; however, gradient descent seems to be inefficient for the optimization of long paths.
Several randomizod path planners have been proposed during the last few years. Their attractiveness stems from their applicability to virtually any type of robots, and their empirically observed success. In this paper we attempt to present a unifying view of these planners and to theoretically explain their success. First, we introduce a general planning scheme that consists of randomly sampling the robot' s configuration space. We then describe two previously developed planners as instances of planners based on this scheme, but applying very different sampling strategies. These planners are probabilistically complete: if a path exists, they will find one with high probability, if we let them run long enough. Next, for one of the planners, we analyze the relation between the probability of failure and the running time. Under assumptions characterizing the "goodness" of the robot's free space, we show that the running time only grows as the absolute value of the logarithm of the probability of failure that we are willing to tolerate. We also show that it increases at a reasonable rate as the space goodness degrades. In the last section we suggest directions for future research.