8,312 research outputs found
Efficient Algorithms for Asymptotic Bounds on Termination Time in VASS
Vector Addition Systems with States (VASS) provide a well-known and
fundamental model for the analysis of concurrent processes, parameterized
systems, and are also used as abstract models of programs in resource bound
analysis. In this paper we study the problem of obtaining asymptotic bounds on
the termination time of a given VASS. In particular, we focus on the
practically important case of obtaining polynomial bounds on termination time.
Our main contributions are as follows: First, we present a polynomial-time
algorithm for deciding whether a given VASS has a linear asymptotic complexity.
We also show that if the complexity of a VASS is not linear, it is at least
quadratic. Second, we classify VASS according to quantitative properties of
their cycles. We show that certain singularities in these properties are the
key reason for non-polynomial asymptotic complexity of VASS. In absence of
singularities, we show that the asymptotic complexity is always polynomial and
of the form , for some integer , where is the
dimension of the VASS. We present a polynomial-time algorithm computing the
optimal . For general VASS, the same algorithm, which is based on a complete
technique for the construction of ranking functions in VASS, produces a valid
lower bound, i.e., a such that the termination complexity is .
Our results are based on new insights into the geometry of VASS dynamics, which
hold the potential for further applicability to VASS analysis.Comment: arXiv admin note: text overlap with arXiv:1708.0925
On Time Optimization of Centroidal Momentum Dynamics
Recently, the centroidal momentum dynamics has received substantial attention
to plan dynamically consistent motions for robots with arms and legs in
multi-contact scenarios. However, it is also non convex which renders any
optimization approach difficult and timing is usually kept fixed in most
trajectory optimization techniques to not introduce additional non convexities
to the problem. But this can limit the versatility of the algorithms. In our
previous work, we proposed a convex relaxation of the problem that allowed to
efficiently compute momentum trajectories and contact forces. However, our
approach could not minimize a desired angular momentum objective which
seriously limited its applicability. Noticing that the non-convexity introduced
by the time variables is of similar nature as the centroidal dynamics one, we
propose two convex relaxations to the problem based on trust regions and soft
constraints. The resulting approaches can compute time-optimized dynamically
consistent trajectories sufficiently fast to make the approach realtime
capable. The performance of the algorithm is demonstrated in several
multi-contact scenarios for a humanoid robot. In particular, we show that the
proposed convex relaxation of the original problem finds solutions that are
consistent with the original non-convex problem and illustrate how timing
optimization allows to find motion plans that would be difficult to plan with
fixed timing.Comment: 7 pages, 4 figures, ICRA 201
Projection methods in conic optimization
There exist efficient algorithms to project a point onto the intersection of
a convex cone and an affine subspace. Those conic projections are in turn the
work-horse of a range of algorithms in conic optimization, having a variety of
applications in science, finance and engineering. This chapter reviews some of
these algorithms, emphasizing the so-called regularization algorithms for
linear conic optimization, and applications in polynomial optimization. This is
a presentation of the material of several recent research articles; we aim here
at clarifying the ideas, presenting them in a general framework, and pointing
out important techniques
An Inverse Dynamics Approach to Control Lyapunov Functions
With the goal of moving towards implementation of increasingly dynamic behaviors on underactuated systems, this paper presents an optimization-based approach for solving full-body dynamics based controllers on underactuated bipedal robots. The primary focus of this paper is on the development of an alternative approach to the implementation of controllers utilizing control Lyapunov function based quadratic programs. This approach utilizes many of the desirable aspects from successful inverse dynamics based controllers in the literature, while also incorporating a variant of control Lyapunov functions that renders better convergence in the context of tracking outputs. The principal benefits of this formulation include a greater ability to add costs which regulate the resulting behavior of the robot. In addition, the model error-prone inertia matrix is used only once, in a non-inverted form. The result is a successful demonstration of the controller for walking in simulation, and applied on hardware in real-time for dynamic crouching
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