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On the Collision Detection Problem of Two Moving Objects Described by Algebraic Sets

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Abstract

In this paper, the collision problem of two moving objects is investigated. The objects are described by two algebraic sets (ellipses or circles in the paper). The collision problem discussed involves both static and dynamic case. The static case is that each object moves with known velocity. We use nonlinear programming to decide whether the objects collide. The dynamic case is that each object is controlled by a constraint external force which can be regulated online. For the dynamic case, the collision problem can be modelled as a Minmax problem which can be solved by using differential games. If collision occurs, the time and place of the first collision are given. The moving trajectories are provided in the paper.

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References

  1. G. E. Collins H. Hong (1991) ArticleTitlePartial cylindrical algebraic decomposition for quantifier elimination Journal of Symbolic Computation 12 299–328 Occurrence Handle10.1016/S0747-7171(08)80152-6

    Article  Google Scholar 

  2. Wen-Tsun Wu, On problems involving inequalities, Mathematics-Mechanization Research Preprints, Institute of Systems Science, Academia Sinica, No.7, 1992.

  3. Tianjiao Wu, On a collision problem, Mathematics-Mechanization Research Preprints, Institute of Systems Science, Academia Sinica, No.7, 1992.

  4. Li Dengfeng (2000) Differential Games and Its Applications National Defence Industry Press Beijing

    Google Scholar 

  5. Choi Dong-Soo Kim Seung-Jean Ha In-Joong (2003) ArticleTitleA phase-plane approach to time-optimal control of single-DOF mechanical systems with friction Automatica 39 1407–1415 Occurrence Handle10.1016/S0005-1098(03)00112-2

    Article  Google Scholar 

  6. Wang Chaozhu Qin Huashu (2003) Optimal Control Theory Science Press Beijing

    Google Scholar 

  7. Wu Wen-Tsun (1994) ArticleTitleOn a finiteness theorem about problems involving inequalities Sys. Sci. & Math. Sci. 7 IssueID3 193–200

    Google Scholar 

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Authors and Affiliations

  1. College of Information and Controlling Engineering, University of Petroleum (East China), Dongying, 257061, China

    Shurong Li & Chunwang Hou

Authors
  1. Shurong Li
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  2. Chunwang Hou
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Corresponding author

Correspondence to Shurong Li.

Additional information

Partially supported by a National Key Basic Research Project of China (2004CB318000).

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Li, S., Hou, C. On the Collision Detection Problem of Two Moving Objects Described by Algebraic Sets. Jrl Syst Sci & Complex 20, 108–118 (2007). https://doi.org/10.1007/s11424-007-9009-2

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  • DOI: https://doi.org/10.1007/s11424-007-9009-2

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