656 research outputs found
Provably Robust Semi-Infinite Program Under Collision Constraints via Subdivision
We present a semi-infinite program (SIP) solver for trajectory optimizations
of general articulated robots. These problems are more challenging than
standard Nonlinear Program (NLP) by involving an infinite number of non-convex,
collision constraints. Prior SIP solvers based on constraint sampling cannot
guarantee the satisfaction of all constraints. Instead, our method uses a
conservative bound on articulated body motions to ensure the solution
feasibility throughout the optimization procedure. We further use subdivision
to adaptively reduce the error in conservative motion estimation. Combined, we
prove that our SIP solver guarantees feasibility while approaches the critical
point of SIP problems up to arbitrary user-provided precision. We have verified
our method on a row of trajectory optimization problems involving industrial
robot arms and UAVs, where our method can generate collision-free, locally
optimal trajectories within a couple minutes
Synthesis of Switching Protocols from Temporal Logic Specifications
We propose formal means for synthesizing switching protocols that determine the sequence in which the modes of a switched system are activated to satisfy certain high-level specifications in linear temporal logic. The synthesized protocols are robust against exogenous disturbances on the continuous dynamics. Two types of finite transition systems, namely under- and over-approximations, that abstract the behavior of the underlying continuous dynamics are defined. In particular, we show that the discrete synthesis problem for an under-approximation can be formulated as a model checking problem, whereas that for an over-approximation can be transformed into a two-player game. Both of these formulations are amenable to efficient, off-the-shelf software tools. By construction, existence of a discrete switching strategy for the discrete synthesis problem guarantees the existence of a continuous switching protocol for the continuous synthesis problem, which can be implemented at the continuous level to ensure the correctness of the nonlinear switched system. Moreover, the proposed framework can be straightforwardly extended to accommodate specifications that require reacting to possibly adversarial external events. Finally, these results are illustrated using three examples from different application domains
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