2. A brief summary of our chosen previous studies related to walking robots

Our numerical investigations related to the kinematical analysis and control of the six-legged walking robot have been initiated in the paper [4]. To control the movement of the tip of the robot leg, a nonlinear mechanical oscillator describing

## On the Controlling of Multi-Legged Walking Robots on Stable and Unstable Ground DOI: http://dx.doi.org/10.5772/intechopen.90208

stick–slip mechanical vibrations has been proposed and applied as the central pattern generator (CPG). By using also three well-known mechanical oscillators (i.e., Hopf oscillator, Van der Pol oscillator, and Rayleigh oscillator), the advantages of the proposed CPG model have been illustrated and discussed. Time histories of the articulated variables in all joints of the robot's leg and its configurations during walking indicated some analogies between the characteristics of the simulated walking robot and animals found in nature. Eventually, the results obtained in that paper indicated that, from the point of view of the energy demand, the proposed model of CPG based on the stick–slip vibrations can be more efficient than other previous CPG models found in the literature.

In the next paper [5], the above-presented study has been continued regarding power consumption experimental analysis with the use of the constructed hexapod robot controlled by previously introduced CPGs. The power consumption of the constructed robot has been calculated based on the current consumption in the servo motors, which drive the robot's legs. The performed experimental investigations showed different energy demand, depending on the CPG model driving the robot's legs. By comparing the total energy demand of all servomechanisms installed in the robot for the same locomotion conditions, it has been proven that the proposed CPG model is characterized by the lowest energy demand.

The study [6] introduced dynamical modeling of the previously investigated hexapod robot walking with the tripod gait on a planar and hard ground. This type of gait is commonly used by six-legged real insects as well as six-legged walking machines met in engineering applications. Using the inverse dynamic approach and some simplifications resulting from the symmetry of the robot, vertical components of the ground reaction forces acting on the robot's legs have been estimated numerically. As a result, different time histories of the contact forces and overloads acting on the robot's legs have been detected, depending on the CPG model driving the robot's legs. Finally, the obtained information can be used for further strength analysis of the robot's legs to ensure trouble-free use and an extension of life and operational time of the robot.

On the contrary to the abovementioned papers, in Ref. [7], a new model of an octopod (eight-legged) robot has been developed and numerically simulated in order to investigate crucial kinematic parameters during locomotion with the tetrapod gait, i.e., similar gait as the tripod gait used in hexapod robots. Another wellknown CPG model has also been used (i.e., CPG model constructed based on the Toda-Rayleigh lattice). However, the main novelty of that article is a proposition of a new model of gait generator constructed based on the sine function, further referred as a SINE generator. The proposed model of gait is relatively simple in comparison with other control methods found in the literature and can be especially useful when the robot walks on planar/regular surfaces. Some advantages of the proposed SINE generator have been outlined, including the lack of the acceleration and deceleration of the robot gravity center. These advantages have a positive influence on the robot's dynamics, especially when it comes to the minimization of the ground reaction forces acting on the robot's legs and low energy consumption of the robot during walking.

Numerical investigations of the octopod robot and a novel gait generator introduced in the paper [7] have been significantly extended in Ref. [8]. Aside from computing crucial kinematic parameters of the robot, also time histories of the robot's dynamic locomotion parameters have been illustrated and discussed. The obtained dynamic parameters confirmed some advantages of the proposed SINE generator previously presented in paper [7]. Concluding, it should be mentioned that the proposed SINE generator is relatively simple in comparison with other control methods found in the literature. Especially, solving of nonlinear differential

## Dynamical Systems Theory

equations is not required in this model, on the contrary to all previously presented CPGs. The proposed model of the gait does not produce the unnecessary fluctuations in the center of gravity of the robot or variations in the acceleration/deceleration in the direction of the robot movement. This is why the proposed generator appears to be more efficient with respect to the energy demand than other CPGs investigated in that paper.

In the next paper [9], another kinematic/dynamic simulation model of the hexapod robot has been developed and implemented in Mathematica. On the contrary to previous crab-like hexapod/octopod robots, another kinematic model of a single robot's leg has been used. Also in that study, advantages of the proposed gait generator have been clearly emphasized, especially with regard to the kinematic parameters (displacement and velocity of the whole robot) as well as dynamic parameters (ground reaction forces and overloads acting on the robot legs). In addition, the problem of trajectory planning of the position of the robot body during the walking process has been considered. In the developed simulation model, the appropriate fluctuations of the robot in the vertical direction during the walking process can be controlled precisely. Such a control approach can be useful in the natural environment, for instance, when the robot is walking under or over obstacles.

In paper [10], novel kinematic and dynamic models of a mammal-like octopod robot have been developed and numerically investigated. In order to control the robot's legs, also new simple gait generators constructed based on a sine function have been employed and tested. The proposed models are relatively simple in comparison to other control methods found in the literature. It has been shown that the used gait generators can be useful to obtain better both kinematic and dynamic properties of motion of the whole robot. The advantages of the proposed models have been clearly emphasized, especially with regard to the crucial kinematic and dynamic parameters. Another novelty of this paper is a proposition of one model to control the initial, regular, and terminal phases of the robot gait without the need for generating additional control signals. The developed simulation model of the robot allows also to precisely control robot's vertical position. As a result, better stability of the whole robot during walking and performing the planned tasks, also on terrains characterized by a relatively low friction coefficient between the ground and the robot feet, has been detected.

The study presented in paper [11] is a significant extension of the control methods introduced in the paper [10]. To drive the robot's legs, also another nonlinear oscillator (i.e., hybrid Van der Pol-Rayleigh oscillator) has been used as a central pattern generator. Moreover, also a new, relatively simple, and efficient model has been proposed and tested. The proposed model of the gait generator is useful to obtain better both kinematic and dynamic parameters of motion of the robot walking in different directions. By changing the length and the height of a single step of the robot, the initial, rhythmic, and terminal phases of the robot gait, as in the previous paper [10], have been introduced. Using the simulation model developed in Mathematica, displacement, velocity and acceleration of the center of the robot's body, fluctuations in the zero moment point of the robot, and the ground reaction forces acting on the feet of the robot have been computed, reported, and discussed. The obtained results showed advantages of the introduced model of robot's gaits regarding fluctuations in the robot's body, the minimum value of dynamic stability margin, as well as the minimum value of a friction coefficient which is necessary to avoid slipping between the ground and the robot's feet during the walking process. Moreover, the proposed model does not produce unnecessary fluctuations in the velocity both in the vertical and horizontal (i.e., movement and lateral) directions of the robot. As a result, it has also a positive impact on the

On the Controlling of Multi-Legged Walking Robots on Stable and Unstable Ground DOI: http://dx.doi.org/10.5772/intechopen.90208

dynamical parameters of the robot. In addition, as some of the previously discussed models, the proposed gait generator is relatively simple in comparison to the other three tested CPGs constructed on the basis of the nonlinear oscillators. Finally, the employed model of gait also allowed to precisely control the vertical position of the robot during walking in different directions.

Also recently, various control strategies of the walking machines were usually tested by other researches using different commercial software such as MATLAB [2, 12, 13], ADAMS [12, 14–16], or the Open Dynamics Engine [17, 18]. It shows that investigations of walking robots are still challenging for researches and focus their attention. Therefore, as it was shortly mentioned above, in this chapter we developed a general full parametric simulation model of a hybrid walking robot, i.e., the robot which can have different numbers of legs inspired biologically by insects, reptiles, or mammals. To drive the legs of the abovementioned robot, we employed central pattern generator, firstly introduced in our previous paper [11]. Moreover, we also used own algorithm, which is suitable for a smooth transition between different gait phases, i.e., initial, rhythmic, and terminal phases [10]. Eventually, we considered the problem of controlling the direction of the movement of the robot and control all six spatial degrees of freedom of the robot's body (three deviations and three rotations along and around three different axes, respectively), as well as control all robot's legs on planar, vibrating, and unstable ground. These control possibilities can be especially helpful in a natural environment of the robot, when it comes to both the navigation and obstacle avoidance.
