Robust Planning with Quadratically Constrained State-Dependent Uncertainties
Abstract
We address robust trajectory-planning problems with state constraints and with control/state-dependent uncertain inputs and measurements. Uncertain inputs and measurements satisfy quadratic inequalities with rank-2 indefinite multipliers; measurements depend on the uncertain-state realization and on the uncertain inputs. By means of Lagrangian duality, we derive finite nonsmooth constraints that guarantee robust satisfaction of the state constraints, yielding a formulation that can be addressed without bilevel solvers. We develop a two-step convex heuristic for the resulting nonconvex nonsmooth formulation, using a convex relaxation followed by a convex feasibility-recovery step. We test the two-step approach on a rendezvous scenario with state-dependent navigation uncertainty, and we reduce by a factor 13.8 the computation time with respect to the commercial solver Gurobi, while maintaining robust satisfaction of constraints.
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BibTeX
@misc{spada2026robust,
title = {{Robust Planning with Quadratically Constrained State-Dependent Uncertainties}},
author = {Fabio Spada and Behçet Açıkmeşe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38803},
eprint = {2609.38803},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38803},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Robust Planning with Quadratically Constrained State-Dependent Uncertainties
AU - Fabio Spada
AU - Behçet Açıkmeşe
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.38803
UR - https://arxiv.org/abs/2609.38803
AB - We address robust trajectory-planning problems with state constraints and with control/state-dependent uncertain inputs and measurements. Uncertain inputs and measurements satisfy quadratic inequalities with rank-2 indefinite multipliers; measurements depend on the uncertain-state realization and on the uncertain inputs. By means of Lagrangian duality, we derive finite nonsmooth constraints that guarantee robust satisfaction of the state constraints, yielding a formulation that can be addressed without bilevel solvers. We develop a two-step convex heuristic for the resulting nonconvex nonsmooth formulation, using a convex relaxation followed by a convex feasibility-recovery step. We test the two-step approach on a rendezvous scenario with state-dependent navigation uncertainty, and we reduce by a factor 13.8 the computation time with respect to the commercial solver Gurobi, while maintaining robust satisfaction of constraints.
ER -