The paper is devoted to trajectory optimization for an inertial object moving in a plane with thrust bounded in absolute value in the presence of external forces. The aim is to maximize the longitudinal terminal velocity with the state constraint satisfied at each time to avoid a lateral collision with an obstacle. The linear tangent law is used as the basis for an algorithm that controls the direction of the thrust. Conditions for the existence of a solution are studied. Constraints on the initial lateral velocity and the time of the motion of the object are obtained. Since the linear tangent law violates the constraint for some motion times, a modified control law is proposed. A transcendental equation is obtained to find a critical value of time above which an undesired collision occurs. The corresponding conjecture is formulated, which allows us to eliminate the ambiguity that arises during the solution process. A method for solving the problem is presented and confirmed by numerical calculations.
Keywords: trajectory optimization, state constraint, velocity maximization, linear tangent law
Received March 3, 2024
Revised March 21, 2024
Accepted March 25, 2024
Funding Agency: This work was performed at the Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences and was supported by the Russian Science Foundation (project no. 23-11-00128, https://rscf.ru/project/23-11-00128/).
Sergey Aleksandrovich Reshmin, Dr. Phys.-Math. Sci., Corresponding Member of RAS, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia, e-mail: reshmin@ipmnet.ru
Madina Timurovna Bektybaeva, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, Moscow, 119526 Russia; doctoral student, the Department of Mechanics and Control Processes, RUDN University, Moscow, 117198 Russia, e-mail: madi8991@mail.ru
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Cite this article as: S.A. Reshmin, M.T. Bektybaeva. Control of acceleration of a dynamic object by the modified linear tangent law in the presence of a state constraint. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 2, pp. 152–163. Proceedings of the Steklov Institute of Mathematics, 2024, Vol. 325, Suppl. 1, pp. S168-S178.
