243 research outputs found
FaSTrack: a Modular Framework for Real-Time Motion Planning and Guaranteed Safe Tracking
Real-time, guaranteed safe trajectory planning is vital for navigation in
unknown environments. However, real-time navigation algorithms typically
sacrifice robustness for computation speed. Alternatively, provably safe
trajectory planning tends to be too computationally intensive for real-time
replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that
achieves both real-time replanning and guaranteed safety. In this framework,
real-time computation is achieved by allowing any trajectory planner to use a
simplified \textit{planning model} of the system. The plan is tracked by the
system, represented by a more realistic, higher-dimensional \textit{tracking
model}. We precompute the tracking error bound (TEB) due to mismatch between
the two models and due to external disturbances. We also obtain the
corresponding tracking controller used to stay within the TEB. The
precomputation does not require prior knowledge of the environment. We
demonstrate FaSTrack using Hamilton-Jacobi reachability for precomputation and
three different real-time trajectory planners with three different
tracking-planning model pairs.Comment: Published in the IEEE Transactions on Automatic Contro
Failing with Grace: Learning Neural Network Controllers that are Boundedly Unsafe
In this work, we consider the problem of learning a feed-forward neural
network (NN) controller to safely steer an arbitrarily shaped planar robot in a
compact and obstacle-occluded workspace. Unlike existing methods that depend
strongly on the density of data points close to the boundary of the safe state
space to train NN controllers with closed-loop safety guarantees, we propose an
approach that lifts such assumptions on the data that are hard to satisfy in
practice and instead allows for graceful safety violations, i.e., of a bounded
magnitude that can be spatially controlled. To do so, we employ reachability
analysis methods to encapsulate safety constraints in the training process.
Specifically, to obtain a computationally efficient over-approximation of the
forward reachable set of the closed-loop system, we partition the robot's state
space into cells and adaptively subdivide the cells that contain states which
may escape the safe set under the trained control law. To do so, we first
design appropriate under- and over-approximations of the robot's footprint to
adaptively subdivide the configuration space into cells. Then, using the
overlap between each cell's forward reachable set and the set of infeasible
robot configurations as a measure for safety violations, we introduce penalty
terms into the loss function that penalize this overlap in the training
process. As a result, our method can learn a safe vector field for the
closed-loop system and, at the same time, provide numerical worst-case bounds
on safety violation over the whole configuration space, defined by the overlap
between the over-approximation of the forward reachable set of the closed-loop
system and the set of unsafe states. Moreover, it can control the tradeoff
between computational complexity and tightness of these bounds. Finally, we
provide a simulation study that verifies the efficacy of the proposed scheme
- …