1,688 research outputs found
Control Barrier Function Based Quadratic Programs for Safety Critical Systems
Safety critical systems involve the tight coupling between potentially
conflicting control objectives and safety constraints. As a means of creating a
formal framework for controlling systems of this form, and with a view toward
automotive applications, this paper develops a methodology that allows safety
conditions -- expressed as control barrier functions -- to be unified with
performance objectives -- expressed as control Lyapunov functions -- in the
context of real-time optimization-based controllers. Safety conditions are
specified in terms of forward invariance of a set, and are verified via two
novel generalizations of barrier functions; in each case, the existence of a
barrier function satisfying Lyapunov-like conditions implies forward invariance
of the set, and the relationship between these two classes of barrier functions
is characterized. In addition, each of these formulations yields a notion of
control barrier function (CBF), providing inequality constraints in the control
input that, when satisfied, again imply forward invariance of the set. Through
these constructions, CBFs can naturally be unified with control Lyapunov
functions (CLFs) in the context of a quadratic program (QP); this allows for
the achievement of control objectives (represented by CLFs) subject to
conditions on the admissible states of the system (represented by CBFs). The
mediation of safety and performance through a QP is demonstrated on adaptive
cruise control and lane keeping, two automotive control problems that present
both safety and performance considerations coupled with actuator bounds
Barrier Functions in Cascaded Controller: Safe Quadrotor Control
Safe control for inherently unstable systems such as quadrotors is crucial.
Imposing multiple dynamic constraints simultaneously on the states for safety
regulation can be a challenging problem. In this paper, we propose a quadratic
programming (QP) based approach on a cascaded control architecture for
quadrotors to enforce safety. Safety regions are constructed using control
barrier functions (CBF) while explicitly considering the nonlinear
underactuated dynamics of the quadrotor. The safety regions constructed using
CBFs establish a non-conservative forward invariant safe region for quadrotor
navigation. Barriers imposed across the cascaded architecture allows
independent safety regulation in quadrotor's altitude and lateral domains.
Despite barriers appearing in a cascaded fashion, we show preservation of
safety for quadrotor motion in SE(3). We demonstrate the feasibility of our
method on a quadrotor in simulation with static and dynamic constraints
enforced on position and velocity spaces simultaneously.Comment: Submitted to ACC 2020, 8 pages, 7 figure
Compositional Set Invariance in Network Systems with Assume-Guarantee Contracts
This paper presents an assume-guarantee reasoning approach to the computation
of robust invariant sets for network systems. Parameterized signal temporal
logic (pSTL) is used to formally describe the behaviors of the subsystems,
which we use as the template for the contract. We show that set invariance can
be proved with a valid assume-guarantee contract by reasoning about individual
subsystems. If a valid assume-guarantee contract with monotonic pSTL template
is known, it can be further refined by value iteration. When such a contract is
not known, an epigraph method is proposed to solve for a contract that is
valid, ---an approach that has linear complexity for a sparse network. A
microgrid example is used to demonstrate the proposed method. The simulation
result shows that together with control barrier functions, the states of all
the subsystems can be bounded inside the individual robust invariant sets.Comment: Submitted to 2019 American Control Conferenc
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