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Continuous and discrete abstractions for planning, applied to ship docking⁎This work was supported by the Peder Sather Center for Advanced Study, a consortium of UC Berkeley and nine Norwegian academic institutions. It was also supported in part by the U.S. National Science Foundation grant ECCS-1906164, the U.S. Air Force Office of Scientific Research grant FA9550-18-1-0253, and Research Council of Norway through the Centres of Excellence funding scheme, project number 223254 AMOS, FRINATEK project 274441 UNLOCK, and MAROFF project 280655 ORCAS. Issue 2 (2020)
Record Type:
Journal Article
Title:
Continuous and discrete abstractions for planning, applied to ship docking⁎This work was supported by the Peder Sather Center for Advanced Study, a consortium of UC Berkeley and nine Norwegian academic institutions. It was also supported in part by the U.S. National Science Foundation grant ECCS-1906164, the U.S. Air Force Office of Scientific Research grant FA9550-18-1-0253, and Research Council of Norway through the Centres of Excellence funding scheme, project number 223254 AMOS, FRINATEK project 274441 UNLOCK, and MAROFF project 280655 ORCAS. Issue 2 (2020)
Main Title:
Continuous and discrete abstractions for planning, applied to ship docking⁎This work was supported by the Peder Sather Center for Advanced Study, a consortium of UC Berkeley and nine Norwegian academic institutions. It was also supported in part by the U.S. National Science Foundation grant ECCS-1906164, the U.S. Air Force Office of Scientific Research grant FA9550-18-1-0253, and Research Council of Norway through the Centres of Excellence funding scheme, project number 223254 AMOS, FRINATEK project 274441 UNLOCK, and MAROFF project 280655 ORCAS.
Abstract: We propose a hierarchical control framework for the synthesis of correct-by-construction controllers for nonlinear control-affine systems with respect to reach-avoid-stay specifications. We first create a low-dimensional continuous abstraction of the system and use Sum-of-Squares (SOS) programming to obtain a low-level controller ensuring a bounded error between the two models. We then create a discrete abstraction of the continuous abstraction and use formal methods to synthesize a controller satisfying the specifications shrunk by the obtained error bound. Combining both controllers finally solves the main control problem on the initial system. This two-step framework allows the discrete abstraction methods to deal with higher-dimensional systems which may be computationally expensive without the prior continuous abstraction. The main novelty of the proposed SOS continuous abstraction is that it allows the error between abstract and concrete models to explicitly depend on the control input of the abstract model, which offers more freedom in the choice of the continuous abstraction model and provides lower error bounds than when only the states of both models are considered. This approach is illustrated on the docking problem of a marine vessel.