The walking mobile robots (WMR) have recently become widely popular in robotics. They are especially useful in the extreme cases: search and rescue operations; cargo delivery over highly rough terrain; building a map. These robots also serve to explore and describe a partially or completely non-deterministic workspace, as well as to explore areas that are dangerous to human life. One of the main requirements for these WMR is the robustness of its control system. It allows WMR to maintain the operability when the characteristics of the support surface change as well as under more severe conditions, in particular, loss of controllability or damage of the supporting limb (SL). We propose to use the principles of genetic programming to create a WMR control system that allows a robot to adapt to possible changes in its kinematics, as well as to the characteristics of the support surface on which it moves. This approach does not require strong computational power or a strict formal classification of possible damage to the WMR. This article discusses two main WMR control modes: standard, which accord to a serviceable kinematics, and emergency, in which one or more SL drives are damaged or lost controllability. As an example, the structure of the control system of the WMP is proposed, the kinematics of which is partially destroyed in the process of movement. We developed a method for controlling such robot, which is based on the use of a genetic algorithm in conjunction with the Mealy machine. Modeling of modes of movement of WMR with six SL was carried out in the V-REP program for two cases of injury: absent and not functioning limb. We present the results of simulation of emergency gaits for these configurations of WMP and the effectiveness of the proposed method in the case of damage to the kinematic scheme. We also compared the performance of the genetic algorithm for the damaged WMR with the standard control algorithm.
On the singularity structure of Kahan discretizations of a class of quadratic vector fields