34 research outputs found
Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case
Motion planning under differential constraints is a classic problem in
robotics. To date, the state of the art is represented by sampling-based
techniques, with the Rapidly-exploring Random Tree algorithm as a leading
example. Yet, the problem is still open in many aspects, including guarantees
on the quality of the obtained solution. In this paper we provide a thorough
theoretical framework to assess optimality guarantees of sampling-based
algorithms for planning under differential constraints. We exploit this
framework to design and analyze two novel sampling-based algorithms that are
guaranteed to converge, as the number of samples increases, to an optimal
solution (namely, the Differential Probabilistic RoadMap algorithm and the
Differential Fast Marching Tree algorithm). Our focus is on driftless
control-affine dynamical models, which accurately model a large class of
robotic systems. In this paper we use the notion of convergence in probability
(as opposed to convergence almost surely): the extra mathematical flexibility
of this approach yields convergence rate bounds - a first in the field of
optimal sampling-based motion planning under differential constraints.
Numerical experiments corroborating our theoretical results are presented and
discussed
Optimal Sampling-Based Motion Planning under Differential Constraints: the Drift Case with Linear Affine Dynamics
In this paper we provide a thorough, rigorous theoretical framework to assess
optimality guarantees of sampling-based algorithms for drift control systems:
systems that, loosely speaking, can not stop instantaneously due to momentum.
We exploit this framework to design and analyze a sampling-based algorithm (the
Differential Fast Marching Tree algorithm) that is asymptotically optimal, that
is, it is guaranteed to converge, as the number of samples increases, to an
optimal solution. In addition, our approach allows us to provide concrete
bounds on the rate of this convergence. The focus of this paper is on mixed
time/control energy cost functions and on linear affine dynamical systems,
which encompass a range of models of interest to applications (e.g.,
double-integrators) and represent a necessary step to design, via successive
linearization, sampling-based and provably-correct algorithms for non-linear
drift control systems. Our analysis relies on an original perturbation analysis
for two-point boundary value problems, which could be of independent interest
Closing the Loop on Runtime Monitors with Fallback-Safe MPC
When we rely on deep-learned models for robotic perception, we must recognize
that these models may behave unreliably on inputs dissimilar from the training
data, compromising the closed-loop system's safety. This raises fundamental
questions on how we can assess confidence in perception systems and to what
extent we can take safety-preserving actions when external environmental
changes degrade our perception model's performance. Therefore, we present a
framework to certify the safety of a perception-enabled system deployed in
novel contexts. To do so, we leverage robust model predictive control (MPC) to
control the system using the perception estimates while maintaining the
feasibility of a safety-preserving fallback plan that does not rely on the
perception system. In addition, we calibrate a runtime monitor using recently
proposed conformal prediction techniques to certifiably detect when the
perception system degrades beyond the tolerance of the MPC controller,
resulting in an end-to-end safety assurance. We show that this control
framework and calibration technique allows us to certify the system's safety
with orders of magnitudes fewer samples than required to retrain the perception
network when we deploy in a novel context on a photo-realistic aircraft taxiing
simulator. Furthermore, we illustrate the safety-preserving behavior of the MPC
on simulated examples of a quadrotor. We open-source our simulation platform
and provide videos of our results at our project page:
https://tinyurl.com/fallback-safe-mpc.Comment: Accepted to the 2023 IEEE Conference on Decision and Contro
Leveraging Compositional Methods for Modeling and Verification of an Autonomous Taxi System
We apply a compositional formal modeling and verification method to an
autonomous aircraft taxi system. We provide insights into the modeling approach
and we identify several research areas where further development is needed.
Specifically, we identify the following needs: (1) semantics of composition of
viewpoints expressed in different specification languages, and tools to reason
about heterogeneous declarative models; (2) libraries of formal models for
autonomous systems to speed up modeling and enable efficient reasoning; (3)
methods to lift verification results generated by automated reasoning tools to
the specification level; (4) probabilistic contract frameworks to reason about
imperfect implementations; (5) standard high-level functional architectures for
autonomous systems; and (6) a theory of higher-order contracts. We believe that
addressing these research needs, among others, could improve the adoption of
formal methods in the design of autonomous systems including learning-enabled
systems, and increase confidence in their safe operations.Comment: 2023 International Conference on Assured Autonomy (ICAA