1,976 research outputs found
Hierarchical Time-Optimal Planning for Multi-Vehicle Racing
This paper presents a hierarchical planning algorithm for racing with
multiple opponents. The two-stage approach consists of a high-level behavioral
planning step and a low-level optimization step. By combining discrete and
continuous planning methods, our algorithm encourages global time optimality
without being limited by coarse discretization. In the behavioral planning
step, the fastest behavior is determined with a low-resolution spatio-temporal
visibility graph. Based on the selected behavior, we calculate maneuver
envelopes that are subsequently applied as constraints in a time-optimal
control problem. The performance of our method is comparable to a parallel
approach that selects the fastest trajectory from multiple optimizations with
different behavior classes. However, our algorithm can be executed on a single
core. This significantly reduces computational requirements, especially when
multiple opponents are involved. Therefore, the proposed method is an efficient
and practical solution for real-time multi-vehicle racing scenarios.Comment: 6 pages, accepted to be published as part of the 26th IEEE
International Conference on Intelligent Transportation Systems (ITSC 2023),
Bilbao, Bizkaia, Spain, September 24-28, 202
Pseudo-Optimal Reduction of Structured DAEs by Rational Interpolation
In this contribution, we extend the concept of inner product
and pseudo-optimality to dynamical systems modeled by
differential-algebraic equations (DAEs). To this end, we derive projected
Sylvester equations that characterize the inner product in
terms of the matrices of the DAE realization. Using this result, we extend the
pseudo-optimal rational Krylov algorithm for ordinary
differential equations to the DAE case. This algorithm computes the globally
optimal reduced-order model for a given subspace of defined by
poles and input residual directions. Necessary and sufficient conditions for
pseudo-optimality are derived using the new formulation of the
inner product in terms of tangential interpolation conditions.
Based on these conditions, the cumulative reduction procedure combined with the
adaptive rational Krylov algorithm, known as CUREd SPARK, is extended to DAEs.
Important properties of this procedure are that it guarantees stability
preservation and adaptively selects interpolation frequencies and reduced
order. Numerical examples are used to illustrate the theoretical discussion.
Even though the results apply in theory to general DAEs, special structures
will be exploited for numerically efficient implementations
Online Time-Optimal Trajectory Planning on Three-Dimensional Race Tracks
We propose an online planning approach for racing that generates the
time-optimal trajectory for the upcoming track section. The resulting
trajectory takes the current vehicle state, effects caused by \acl{3D} track
geometries, and speed limits dictated by the race rules into account. In each
planning step, an optimal control problem is solved, making a
quasi-steady-state assumption with a point mass model constrained by
gg-diagrams. For its online applicability, we propose an efficient
representation of the gg-diagrams and identify negligible terms to reduce the
computational effort. We demonstrate that the online planning approach can
reproduce the lap times of an offline-generated racing line during single
vehicle racing. Moreover, it finds a new time-optimal solution when a deviation
from the original racing line is necessary, e.g., during an overtaking
maneuver. Motivated by the application in a rule-based race, we also consider
the scenario of a speed limit lower than the current vehicle velocity. We
introduce an initializable slack variable to generate feasible trajectories
despite the constraint violation while reducing the velocity to comply with the
rules.Comment: 8 pages, accepted to be published as part of the 34th IEEE
Intelligent Vehicles Symposium (IV), Anchorage, Alaska, USA, June 4-7, 202
Parametric Model Order Reduction of Port-Hamiltonian Systems by Matrix Interpolation
In this paper, parametric model order reduction of linear time-invariant systems by matrix interpolation is adapted to large-scale systems in port-Hamiltonian form. A new weighted matrix interpolation of locally reduced models is introduced in order to preserve the port-Hamiltonian structure, which guarantees the passivity and stability of the interpolated system. The performance of the new method is demonstrated by technical example
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