**5. Overcoming obstacles**

robot can adapt to the obstacle and climb it by attacking it with the feet. It does not need special sensors and control algorithms. This process is illustrated in **Figure 8**. The robot body (round base) collides with the vertical section of the obstacle. Then there is a sliding of the feet on the horizontal terrain and the body is sliding on the vertical obstacle, the arm {3} performs a planer movement. It can be determined the instantaneous center of velocities of the arm {3} by taking into account the motion of points A and B from it. With respect to the absolute coordinate system, the

> *XQ* ¼ *XB* � *L*<sup>3</sup> sin ð Þ *α YQ* ¼ *L*<sup>3</sup> cosð Þ *α*

> > *<sup>Q</sup>* <sup>¼</sup> *<sup>L</sup>*<sup>2</sup>

], and connected to the arm AB, is defined by the system of

*X*0 *<sup>Q</sup>* <sup>¼</sup> *<sup>L</sup>*<sup>3</sup>

 

The relative trajectory of the instantaneous velocity center is also an arc of a

*Instantaneous velocity center and adaptive movements in case of collision between the robot's body and the*

*Y*0 *<sup>Q</sup>* <sup>¼</sup> *<sup>L</sup>*<sup>3</sup> 2

In this situation, the instantaneous velocity center of the arm jumps from point *A0* to point *Q1* and starts to move along an arc of a circle (**Figure 8**). The circle has radius *L3* and center [�*XB*,0] and its equation excluding the angle α, is derived

The relative instantaneous velocity center with respect to the coordinate

*XQ* þ *XB* <sup>2</sup> <sup>þ</sup> *<sup>Y</sup>*<sup>2</sup>

ð Þ *α*

(20)

(22)

<sup>3</sup> (21)

<sup>2</sup> ð Þ cos 2ð Þþ *<sup>α</sup>* <sup>1</sup>

sin 2ð Þ *α*

instantaneous center of velocities of the link AB has coordinates:

 

from (20):

system [*A*0,X<sup>0</sup>

equations

**Figure 8.**

*obstacle.*

**102**

,*Y*<sup>0</sup>

*Collaborative and Humanoid Robots*

*X*0

*Y*0

  *<sup>Q</sup>* <sup>¼</sup> *<sup>L</sup>*<sup>3</sup> sin <sup>2</sup>

*<sup>Q</sup>* ¼ *L*<sup>3</sup> sin ð Þ *α* cosð Þ *α*

!

circle, and its equation is derived from (22) after excluding α:

From the reasoning made so far, it can be seen that depending on the height of the obstacle, it is possible to overcome it when attacking with the body or to adapt to it and attack it with the feet. If the height of the obstacle h0 is less than the maximum height reached by the feet hSmax, several scenarios are possible:


**Figure 9** illustrates 5 stages when climbing an obstacle which differ in the elements of contact between the robot, the obstacle and the terrain.

1.The feet are in contact with the obstacle and the round base with the ground. Because of the rotation of the arm {3} sliding starts between the base and the

**Figure 9.** *Five consecutive stages when climbing an obstacle.*

ground or between the feet and the obstacle. At this stage, it is good to ensure good traction between the feet and the obstacle, which will allow the robot to pull itself towards it.


These stages are described in detail in [20, 21], where simulations and results of various experiments are presented.
