# Article

 Article title POSITION-TRAJECTORY CONTROL OF VEHICLE IN 3D WITH POINT OBSTACLES Authors V.Kh. Pshikhopov, М.Yu. Medvedev, V.A. Krukhmalev Section SECTION V. SYSTEM AND CONTROL POINTS Month, Year 01, 2015 @en Index UDC 681.513.66 DOI Abstract Research of the trajectory of the position-trajectory control system with unstable regimes for obstacle avoidance in an uncertain three-dimensional environment is conducted in this paper. Introduction provides with an overview of control systems based on position-trajectory control law, including obstacle avoidance. A mathematical model of the vehicle is represented by the equations of kinematics and dynamics of rigid bodies. 3d motion of the vehicle motion along the line-wise trajectory is considered. Synthesis of basic position-control controller, providing motion along a straight trajectory at a constant speed is described. Obstacle avoidance is performed by introducing an unstable regime near obstacles. The structure of the system of position-trajectory control system with unstable regimes is presented. Instability is introduced through the dependence of the parameters of the referent equation of the distance to the obstacle. Constraints for yaw and pitch angles of the vehicle are considered indirectly. Simulation results for vehicle control system for stationary obstacles with unstable regimes are presented. A study for ways of implementation of unstable motion near an obstacle is conducted. The options of the equal real and multiple roots and complex roots are considered. The influence of errors on the control system is described. Feasibility estimation is made by the minimum distance to the obstacle and the length of the distance traveled. Recommendations on the choice of the roots of the equation of the closed system of the reference position-trajectory control with unstable motion modes. Also, in the linear case, assessment of the distance to the obstacle, which determines the moment when an unstable regime switching on is provided. Download PDF Keywords Position-trajectory control; unstable motion; obstacle avoidance; 3-dimentional motion. References 1. Pshikhopov V.X. Organizatsiya repellerov pri dvizhenii mobil'nykh robotov v srede s prepyatstviyami [The organization of repellere during the movement of mobile robots in environments with obstacles], Mekhatronika, avtomatizatsiya, upravlenie [Mechatronics, automation, control], 2008, No. 2, pp. 34-41. 2. Pshikhopov V.Kh. Upravlenie podvizhnymi ob"ektami a apriori neformalizovannykh sredakh [Management of mobile objects and a priori non-formal environments], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2008, No. 12 (89), pp. 6-19. 3. Pshikhopov V.Kh., Medvedev M.Yu. 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