83 research outputs found
Safe Sequential Path Planning of Multi-Vehicle Systems via Double-Obstacle Hamilton-Jacobi-Isaacs Variational Inequality
We consider the problem of planning trajectories for a group of vehicles,
each aiming to reach its own target set while avoiding danger zones of other
vehicles. The analysis of problems like this is extremely important
practically, especially given the growing interest in utilizing unmanned
aircraft systems for civil purposes. The direct solution of this problem by
solving a single-obstacle Hamilton-Jacobi-Isaacs (HJI) variational inequality
(VI) is numerically intractable due to the exponential scaling of computation
complexity with problem dimensionality. Furthermore, the single-obstacle HJI VI
cannot directly handle situations in which vehicles do not have a common
scheduled arrival time. Instead, we perform sequential path planning by
considering vehicles in order of priority, modeling higher-priority vehicles as
time-varying obstacles for lower-priority vehicles. To do this, we solve a
double-obstacle HJI VI which allows us to obtain the reach-avoid set, defined
as the set of states from which a vehicle can reach its target while staying
within a time-varying state constraint set. From the solution of the
double-obstacle HJI VI, we can also extract the latest start time and the
optimal control for each vehicle. This is a first application of the
double-obstacle HJI VI which can handle systems with time-varying dynamics,
target sets, and state constraint sets, and results in computation complexity
that scales linearly, as opposed to exponentially, with the number of vehicles
in consideration.Comment: European Control Conference 201
A New Simulation Metric to Determine Safe Environments and Controllers for Systems with Unknown Dynamics
We consider the problem of extracting safe environments and controllers for
reach-avoid objectives for systems with known state and control spaces, but
unknown dynamics. In a given environment, a common approach is to synthesize a
controller from an abstraction or a model of the system (potentially learned
from data). However, in many situations, the relationship between the dynamics
of the model and the \textit{actual system} is not known; and hence it is
difficult to provide safety guarantees for the system. In such cases, the
Standard Simulation Metric (SSM), defined as the worst-case norm distance
between the model and the system output trajectories, can be used to modify a
reach-avoid specification for the system into a more stringent specification
for the abstraction. Nevertheless, the obtained distance, and hence the
modified specification, can be quite conservative. This limits the set of
environments for which a safe controller can be obtained. We propose SPEC, a
specification-centric simulation metric, which overcomes these limitations by
computing the distance using only the trajectories that violate the
specification for the system. We show that modifying a reach-avoid
specification with SPEC allows us to synthesize a safe controller for a larger
set of environments compared to SSM. We also propose a probabilistic method to
compute SPEC for a general class of systems. Case studies using simulators for
quadrotors and autonomous cars illustrate the advantages of the proposed metric
for determining safe environment sets and controllers.Comment: 22nd ACM International Conference on Hybrid Systems: Computation and
Control (2019
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