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A Generalized Mixed-Integer Convex Program for Multilegged Footstep Planning on Uneven Terrain [article]

Bernardo Aceituno-Cabezas, Jose Cappelletto, Juan C. Grieco, and Gerardo Fernandez-Lopez
2017 arXiv   pre-print
This approach leverages Mixed-Integer Convex Programming to account for the non-convex constraints that represent footstep rotation and obstacle avoidance.  ...  This work represents, to the knowledge of the authors, the first successful implementation of a continuous optimization-based multilegged footstep planner.  ...  the introduction of non-convex constraints.  ... 
arXiv:1612.02109v2 fatcat:xla4o3xvwfcahojzrm4immlzpy

Solving non-linear Horn clauses using a linear Horn clause solver [article]

Bishoksan Kafle, John P. Gallagher (Roskilde University and IMDEA Software Institute), Pierre Ganty (IMDEA Software Institute, Spain)
2016 arXiv   pre-print
In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses.  ...  The main algorithm then proceeds by applying the linearisation transformation and solver for linear Horn clauses to a sequence of sets of clauses with successively increasing dimension bound.  ...  Morales for his help with Ciao Prolog foreign language interface and some parts of the implementation.  ... 
arXiv:1607.04459v1 fatcat:wmzg2amv5jamfjnhg3qzmnadce

Review of Multi-Agent Algorithms for Collective Behavior: a Structural Taxonomy [article]

Federico Rossi and Saptarshi Bandyopadhyay and Michael Wolf and Marco Pavone
2018 arXiv   pre-print
possible reasons for the slow adoption of complex distributed coordination algorithms in the field, and we highlight areas for further research and development.  ...  In this paper, we review multi-agent collective behavior algorithms in the literature and classify them according to their underlying mathematical structure.  ...  Sequential Convex Programming can solve non-convex motion planning problems through local convexification and iteration (Morgan et al., 2016) .  ... 
arXiv:1803.05464v1 fatcat:vipkvfdcm5cmjiiwchcqj7czv4

Simple and Fast Interval Assignment Using Nonlinear and Piecewise Linear Objectives [chapter]

Scott A. Mitchell
2014 Proceedings of the 22nd International Meshing Roundtable  
I solve the relaxed (non-integer) problem with this cubic objective. I adaptively bend the objective into a piecewise linear function, which has a nearby mostly-integer optimum.  ...  For variables stuck at non-integer values, I tilt their objective. As a last resort, I introduce wave-like nonlinear constraints to force integrality. In short, I relax, bend, tilt, and wave.  ...  Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S.  ... 
doi:10.1007/978-3-319-02335-9_12 dblp:conf/imr/Mitchell13 fatcat:b33hs3tk2rfixpaevgbtvc5hri

Counterexample- and Simulation-Guided Floating-Point Loop Invariant Synthesis [chapter]

Anastasiia Izycheva, Eva Darulova, Helmut Seidl
2020 Lecture Notes in Computer Science  
Such invariants are a prerequisite for reasoning about the safety and roundoff errors of floating-point programs.  ...  Our procedure generates invariants of the form of a convex polynomial inequality that tightly bounds the values of loop variables.  ...  We would like to thank Sebastian Bruggisser for helping to debug our ellipsoids.  ... 
doi:10.1007/978-3-030-65474-0_8 fatcat:g62rmena2ranrmrobp6jmwqhde

Interval computations, rigour and non-rigour in deterministic continuous global optimization

Ralph Baker Kearfott
2011 Optimization Methods and Software  
Deterministic branch and bound methods for the solution of general nonlinear programs have become increasingly popular during the last decade or two, with increasing computer speed, algorithmic improvements  ...  guidance for research into and implementation of these techniques. (6) Provide some theoretical backing, with examples, for convergence of common relaxation techniques.  ...  Acknowledgements I wish to thank the referees, whose very careful reading and comments led to both significant clarification of the paper and avoidance of embarrassing errors.  ... 
doi:10.1080/10556781003636851 fatcat:hvktuh4z4jb2ncygpmxhu3t5fi

Successive Convexification of Non-Convex Optimal Control Problems with State Constraints

Yuanqi Mao, Daniel Dueri, Michael Szmuk, Behçet Açıkmeşe
2017 IFAC-PapersOnLine  
This paper presents a Successive Convexification ( SCvx ) algorithm to solve a class of non-convex optimal control problems with certain types of state constraints.  ...  Sources of non-convexity may include nonlinear dynamics and non-convex state/control constraints.  ...  CONCLUSION As the paper shows, the proposed successive convexification (SCvx) algorithm with project-and-linearize procedure can solve a class of non-convex optimal control problems by solving a sequence  ... 
doi:10.1016/j.ifacol.2017.08.789 fatcat:eawogtlizzczjd5uyhtk3di7rm

Decoupled multiagent path planning via incremental sequential convex programming

Yufan Chen, Mark Cutler, Jonathan P. How
2015 2015 IEEE International Conference on Robotics and Automation (ICRA)  
We show that the proposed algorithm increases the probability of finding feasible trajectories by 33% for teams of more than three vehicles in non-convex environments.  ...  This paper presents a multiagent path planning algorithm based on sequential convex programming (SCP) that finds locally optimal trajectories.  ...  We also examined why previous SCP-based methods often fail to find feasible trajectories in non-convex domains, as well as why decoupled implementations of SCP-based start goal Iter 1 Iter 2 Iter 5 Iter  ... 
doi:10.1109/icra.2015.7140034 dblp:conf/icra/ChenCH15 fatcat:dmcuib7hbnda3lyooyayemzwsm

Rotational polygon containment and minimum enclosure using only robust 2D constructions

Victor J. Milenkovic
1999 Computational geometry  
A version of the algorithm and implementation also solves rotational minimum enclosure: given a class C of container polygons, find a container C ∈ C of minimum area for which containment has a solution  ...  An algorithm and a robust floating point implementation is given for rotational polygon containment: given polygons P 1 , P 2 , P 3 , . . . , P k and a container polygon C, find rotations and translations  ...  As far as we know, there are no other algorithms for k > 2 or implementations for k 2 for multiple non-convex polygons.  ... 
doi:10.1016/s0925-7721(99)00006-1 fatcat:ubtmhfkmtvdorahhdbvodcdb7e

Distributed implementation of SIGNAL: Scheduling & graph clustering [chapter]

Olivier MaffeÏs, Paul Guernic
1994 Lecture Notes in Computer Science  
This paper introduces the scheduling strategy and some key tools which have been designed for the distributed implementation of Signal, a real-time synchronous data ow language.  ...  These tools are acting on the concept of Synchronous-Flow Dependence Graph (SFD Graph) which de nes a generalization of Directed Acyclic Graph and constitutes the abstract representation of Signal programs  ...  Like in Sarkar's approach, this algorithm performs non-linear clustering.  ... 
doi:10.1007/3-540-58468-4_183 fatcat:afzupi23rvgjfls62svrtfdgrm

Survey of convex optimization for aerospace applications

Xinfu Liu, Ping Lu, Binfeng Pan
2017 Astrodynamics  
Convex optimization is a class of mathematical programming problems with polynomial complexity for which state-of-the-art, highly efficient numerical algorithms with predeterminable computational bounds  ...  Coinciding the strong drive toward autonomous operations of aerospace vehicles, convex optimization has seen rapidly increasing utility in solving aerospace GN&C problems with the potential for onboard  ...  Acknowledgements The author at Beijing Institute of Technology gratefully acknowledges the support to this work by the National Natural Science Foundation of China (Grant No. 61603017).  ... 
doi:10.1007/s42064-017-0003-8 fatcat:sjgmn5eeafdnrauvuoc7ecjdsy

RETALT: Development of an Optimal GNC Solution for Recovery of an Orbital Launch Vehicle

A. Botelho, C. Recupero, V. Fernandez, A. Fabrizi, G. De Zaiacomo
2021 Zenodo  
Within this methodology two approaches are identified, namely single convex optimization and successive convexification, for which a trade-off is performed.  ...  This paper presents the Guidance, Navigation and Control solution currently in development by DEIMOS Space for RETALT (Retro Propulsion Assisted Landing Technologies), an EU Horizon 2020 project for studying  ...  Solving this requires non-linear programming (NLP) algorithms, which are undesirable to use in real-time, since there is typically no guarantee of convergence to a local minimum.  ... 
doi:10.5281/zenodo.5779497 fatcat:hxtnjxg52nck3g3ji7nzzt236u

Goal programming and cognitive biases in decision-making

T J Stewart
2005 Journal of the Operational Research Society  
What in effect happens is that for substantial levels of anchoring (y =0.4), performance of the goal programming algorithm is quite poor for both convex and concave problem structures.  ...  The basic principle underlying goal programming is (generally by implementation of an appropriate mathema- tical programming algorithm) to select x € X and the 6;>0 so as to minimize an aggregate function  ... 
doi:10.1057/palgrave.jors.2601948 fatcat:2mpilfbl5beydcxufhbhacxoqm

Disciplined Convex-Concave Programming [article]

Xinyue Shen and Steven Diamond and Yuantao Gu and Stephen Boyd
2016 arXiv   pre-print
Convex-concave programming is an organized heuristic for solving nonconvex problems that involve objective and constraint functions that are a sum of a convex and a concave term.  ...  In this paper we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP).  ...  DGE-114747, by the DARPA X-DATA and SIMPLEX programs, and by the CSC State Scholarship Fund.  ... 
arXiv:1604.02639v1 fatcat:c6d52pt3pzf6vcoiuo2kjvrciq

Disciplined convex-concave programming

Xinyue Shen, Steven Diamond, Yuantao Gu, Stephen Boyd
2016 2016 IEEE 55th Conference on Decision and Control (CDC)  
Convex-concave programming is an organized heuristic for solving nonconvex problems that involve objective and constraint functions that are a sum of a convex and a concave term.  ...  In this paper we introduce disciplined convex-concave programming (DCCP), which combines the ideas of disciplined convex programming (DCP) with convex-concave programming (CCP).  ...  DGE-114747, by the DARPA X-DATA and SIMPLEX programs, and by the CSC State Scholarship Fund.  ... 
doi:10.1109/cdc.2016.7798400 dblp:conf/cdc/ShenDGB16 fatcat:6ixfvnzdf5gejcfzoe3q6gknmi
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