Theoretical Aspects of the Dynamics of Terrestrial Robotic Complexes With Multifunctional Manipulators in Wheel Drive Mode

A mathematical analysis was conducted and theoretical propositions were developed that describe the dynamics of ground robotic complexes (GRCs) with multifunctional manipulators (MMs) in the wheeled propulsion mode. It was established that a feature of the GRC motion with MMs is that, despite the external similarity to the classical layout scheme of traditional GRCs, the structural features of the MMs allow each of them to be controlled independently, and both the rotation speed and the angle of the axis relative to the horizon can be changed, and the end effector (EF) that plays the role of a wheel can change the radius within certain limits. The equation of motion of the GRC with MMs in the wheeled propulsion mode in the case of accelerated motion for the same distribution of tangential forces between all four MMs was obtained. The obtained differential equation connects the power characteristic of the propulsion unit, the angle of rotation of the MM axis and the speed of the GRC with MMs in the wheeled propulsion mode. Mathematical models were developed that allow finding: the coordinates of the center of mass taking into account its displacement; points of contact of the EF in the wheel mode with the support surface and reaction forces for each МM; the resulting tangential reaction; the moment of inertia of the EF; the energy consumption when the EF transitions from one face to another; the effective value of the rolling radius of the EF under the condition of movement on a completely solid flat surface and estimate the average moment of resistance based on the energy consumption per turn. It was found that the equations of motion of the GRC with MMs are general, as a result of which several important individual cases were noted and obtained: a ratio for uniform movement of the GRC with MMs on a flat surface, neglecting air resistance, from which it follows that the traction moment required to maintain motion is directly proportional to the mass of the GRC with MMs and the radius of the EF. Reducing the latter increases the smoothness of the ride, reduces the required moment, but also reduces the resulting speed and increases the probability of slipping; a ratio that allows you to determine by how much the traction moment should be increased during uniform upward movement (neglecting air resistance); a ratio that describes the acceleration of the GRC with MMs from rest, neglecting air resistance, and the difference between the radii of the KE and the dependence of the radius of the EF on time.