Control method of high-precision soft docking of moving objects using low-accurate values of relative speed and distance

Abstract

An analytical expression is constructed for the main vector of control forces, providing the pursuit of an unpredictably moving object with the purpose of shockless high-precision docking with it or its shockless capture in a finite period of time using low-accurate values of the measured relative velocity and distance. The constructed control ensures the pursuit of the goal on the principle of proportional navigation, brings the pursuing point in a finite time to the “initial position”, which provides the possibility of reducing the distance to the target, and then ensures the subsequent sliding movement of a point from the “initial position” along the line of discontinuity to the origin of the phase coordinate system. To solve the problem with large relative measurement errors, it was proposed to construct a continuous part of the control force, which provides the process of sliding movement of the representative point along the line of discontinuity, as a function, depending on the current values of the relative velocity and distance. The article also analyzes the issue related to the expansion of the class of control forces by introducing some positive parameter in the expression for the continuous component of the control force. The choice of this parameter affects the duration of the rapprochement of the pursued and pursuing points.