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Friction is a phenomenon which occurs commonly in the nature and in mechanical constructions. One can find numerous mathematical models describing friction as a one-dimensional process. On the other hand, the number of models which take into account second dimension is significantly smaller. The paper in hand introduce two-dimensional, dynamical model for orthotropic dry friction. Proposed model obeys maximum dissipation power principle by means of non-linear two-dimensional bristle stiffness. Numerical studies show influence of orthotropic friction on planar oscillator and 2D stick-slip system trajectories. Model is also verified against experimental results. Frictional pair with orthotropic properties have been prepared for laboratory rig which is a spherical pendulum with frictional contact. Comparison between experimental and simulation results shows good similarity, although further validation is required.Friction is a phenomenon which occurs commonly in the nature and in mechanical constructions. One can find numerous mathematical models describing friction as a one-dimensional process. On the other hand, the number of models which take into account second dimension is significantly smaller. The paper in hand introduce two-dimensional, dynamical model for orthotropic dry friction. Proposed model obeys maximum dissipation power principle by means of non-linear two-dimensional bristle stiffness. Numerical studies show influence of orthotropic friction on planar oscillator and 2D stick-slip system trajectories. Model is also verified against experimental results. Frictional pair with orthotropic properties have been prepared for laboratory rig which is a spherical pendulum with frictional contact. Comparison between experimental and simulation results shows good similarity, although further validation is required.

The paper introduces the constructed prototype of the hexapod robot designed based on the biomechanics of insects for inspection and operation applications as well as for different research investigations related to the walking robots. A detailed discussion on the design and realization of mechanical construction, electronic control system and devices installed on the robot body are presented. Moreover, the control problem of the robot legs is studied in detail. In order to find the relationship between movements commonly used by insects legs and stable trajectories of mechanical systems, first we analyze different previous papers and leg movements of real insects. Next, we are focus on the control the robot leg with several oscillators working as a so-called Central Pattern Generator (CPG) and we propose other model of CPG based on the oscillator describing stick-slip induced vibrations. Some advantages of the proposed model are presented and compared with other previous applied mechanical oscillators with help of numerical simulations performed for both single robot leg and the whole robot. In order to confirm the mentioned numerical simulations, the conducted real experiments are described and some interesting results are reported. Both numerical and experimental results indicate some analogies between the characteristics of the simulated walking robot and animals met in nature as well as the benefits of the proposed stick-slip vibrations as a CPG are outlined. Our research work has been preceded by a biological inspiration, scientific literature review devoted to the six-legged insects met in nature as well as various prototypes and methods of control hexapod robots which can be found in engineering applications.

In the paper the control problem of the six-legged walking robot is studied. In order to find the relationship between commonly used by insects gaits (trajectory of the foot point) and stable trajectory of mechanical systems, at first we analyse various previous papers and the gaits of the real insects. For control the motion of the tip of the robot leg a nonlinear mechanical oscillator describing stick-slip induced vibrations further referred as central pattern generator (CPG) has been proposed. The advantages of the proposed model has been presented and compared with other previous applied mechanical oscillators. The possibility of control of the tip of the robot leg via changing parameters characterized oscillator working as a CPG has been discussed. Time series of the joints and configurations of the robot leg during walking are presented. The obtained numerical solutions indicate some analogies between the characteristics of the simulated walking robot and animals found in nature. Moreover, some aspects of an energy efficiency analysis (in order to reduce the energy costs) are discussed for the analysed system and the whole hexapod robot. In particular, we discuss the interplay of the proposed gait patterns and the system energy cost.