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This work is focused on advanced methods of mobile robot's path planning. The theoretical part describes selected graphical methods, which are useful for speeding up the process of finding the shortest paths, for example through reduction of explored nodes of the state space. In the practical part was created simulate environment in the Python language and in this environment, selected algorithms was implemented.

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Abstract   Background:Low back pain has a reported lifetime prevalence of about 70% and tops the list of  years lived with disease in the developed countries. There is still to date areas on the mechanisms driving pain andmovement system impairments not fully understood. For some areas the  research are evident butclinically friendly methods lack. A new test for measuring joint position  sense (JPS) in the lumbar spine is tested forreliability.  Objectives:Aim of this study was to evaluate test-retest reliability on a new test measuring JPS, using two laser pointers attached to the vertebrates off L1 and S1. Design:Cross-sectional observational test-retest. Methods:82 participants, 41 with mechanical low back pain and 41 healthy controls, were tested  for repositioning error two times with 30-60minutes between tests. Movement directions tested  was; Flexion, extension, rotation right and rotation left in sitting. Intraclasscorrelation coefficient  (ICC) was used for measuring relative reliability and standard error ofmeasurement (SEM) for  absolute reliability. Results:ICC in the LBP group ranged from -0,51 – 0,94 and for the whole group -0,19 – 0,84. The SEM in the LBP group ranged from 0,1 – 2,9 (95%CI -5,6 – 6,4) and for the whole group 0,1 – 3,2 (95%CI -6,3 – 6,2). Conclusions:The test-retest reliability of this JPS test shows poor to moderate reliability. Measuring joint positioning sense by using two laser pointers attached to S1 and L1 as in this study has shown not to be reliable enough to be used in clinical tests or research and can therefore not be recommended.