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Blake 等。 - 2018 - Efficient Computation of Collision Probabiliti
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for Safe Motion Planning∗Andrew Blake, Alejandro Bordallo, Majd Hawasly,Abstract
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Efficient Computation of Collision Probabilities
for Safe Motion Planning
∗
Andrew Blake, Alejandro Bordallo, Majd Hawasly,
Svetlin Penkov, Subramanian Ramamoorthy
†
, Alexandre Silva
Abstract— We address the problem of safe motion planning.
As mobile robots and autonomous vehicles become increasingly
more prevalent in human-centered environments, the need
to ensure safety in the sense of guaranteed collision free
behaviour has taken renewed urgency. Achieving this when
perceptual modules provide only noisy estimates of objects
in the environment requires new approaches. Working within
a probabilistic framework for describing the environment,
we present methods for efficiently calculating a probabilistic
risk of collision for a candidate path. This may be used to
stratify a set of candidate trajectories by levels of a safety
threshold. Given such a stratification, based on user-defined
thresholds, motion synthesis techniques could optimise for
secondary criteria with the assurance that a primary safety
criterion is already being satisfied. A key contribution of this
paper is the use of a ‘convolution trick’ to factor the calculation
of integrals providing bounds on collision risk, enabling an O(1)
computation even in cluttered and complex environments.
I. INTRODUCTION
Mobile robotic systems that can autonomously plan their
paths in complex environments are becoming increasingly
more prevalent. An example of such a rapidly emerging
technology is autonomous vehicles that can navigate by
themselves on urban roads. Such vehicles must not only per-
form complex manoeuvres among people and other vehicles,
but they must do this while guaranteeing stringent constraints
on the probability of adverse events occurring, such as
collisions with these other agents in the environments. In one
study [1], it is estimated that publicly deployable autonomous
vehicles must achieve less than 1 collision in hundreds of
millions of miles driven in order for their maximum failure
rates to be established as acceptable.
The sensory input available to such a mobile robot are
typically quite noisy. Typically, the environment is perceived
through sensors such as based on stereo vision or LIDAR,
requiring not only signal processing for smoothing or noise
removal, but also the use of more complex ‘object finding’
algorithms to discern drivable surfaces or other agents in
the environment. State of the art algorithms achieving such
capability tend to be based on methods that imply a limit
on the achievable accuracy and reliability of detections [2],
[3]. Therefore, we can only treat such perception modules
as being able to provide us with a probability distribution
[4] over poses of the various objects in the scene. Achieving
safe motion planning in such a setting will require the motion
planning methods to turn these into probabilities of unsafe
All authors are affiliated with FiveAI Ltd., Edinburgh, UK; Authors are
listed in alphabetical order.
†
Corresponding author: s.ramamoorthy@five.ai
events (such as a collision of the robot with another agent),
providing at least approximate assurance regarding the (non-
)occurrence of these events.
Fig. 1: A visualisation of the motion planning problem
faced by our robot. The three curves represent possible
paths, π, that the robot could traverse. The environment
is represented by the two white cars, whose position is
known only via probabilities, depicted by the distributions
(over the centroids). The outcome of our computations is an
assignment of risk of collision to each curve, as in equations
3, 4, which defines a rank ordering (here, blue is most
preferred and red is least preferred).
A. Problem Formulation
The core problem that concerns us in this paper is that of
safe motion planning in an imprecisely known environment.
As input, we assume detection of objects in the environment
along with probability distributions over pose, such as over
their centroid position when the shape model is known. This
defines the space within which we must search over paths. In
our formulation, the first step is to determine the probability
of a collision event occurring (i.e., the spatial extent of
the robot and the spatial extent of any obstacle having
an overlap) along any given path. This core computation
may then be used to modify a variety of motion synthesis
methods. For instance, the Rapidly-exploring Random Tree
(RRT) algorithm can utilise this probability within the search
process. Likewise, a variational formulation of optimal con-
trol [5] could include this within the cost terms.
B. Related Work
The issue of safety in control and motion planning has
been investigated from a number of different methodological
arXiv:1804.05384v1 [cs.RO] 15 Apr 2018
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