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Ground cover is more difficult to define, especially in the case of sand, because it can t be scaled. Sand is just sand no matter what size the vehicle is (except for tiny robots of course), and mud is still mud. Driving on sand or mud would then be a function of ground pressure, the maximum force the vehicle can exert on a wheel, track, or foot, divided by the area that a supporting element places on the ground. Lower ground pressure reduces the amount the driving element sinks, thereby reducing the amount of power required to move that element. Higher ground pressure is helpful in only two cases: towing a heavy load behind the robot, and climbing steep slopes. Robots are infrequently required to be tow trucks, but this may change as the variety of tasks they are put to widens. Climbing hills, though, is a common task. The effect of ground pressure on hill climbing can be overcome with careful tread design (independent of the mobility system), which combines the benefits of low ground pressure with high traction. Lower ground pressure should be considered to indicate a more capable mobility system. The theory that sand and mud are not scalable can t be applied to grass however, because tall field grass really is significantly larger than short lawn grass. Grass seems benign, but it is strong enough when bunched up to throw tracks, stall wheeled vehicles, and trip walkers. These problems can be roughly related to ground pressure since a lighter pressure system would tend to ride higher on wet grass, reducing its tangling problems. The problems caused by grass, then, can be assumed to be effectively covered by the ground pressure category.



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The network shown in Fig. 4-4(a) contains ve nodes, where 4 and 5 are simple nodes and 1, 2, and 3 are principal nodes. In the node voltage method, one of the principal nodes is selected as the reference and equations based on KCL are written at the other principal nodes. At each of these other principal nodes, a voltage is assigned, where it is understood that this is a voltage with respect to the reference node. These voltages are the unknowns and, when determined by a suitable method, result in the network solution.

Fig. 4-4

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The network is redrawn in Fig. 4-4(b) and node 3 selected as the reference for voltages V1 and V2 . KCL requires that the total current out of node 1 be zero: V1 Va V1 V1 V2 0 RA RB RC Similarly, the total current out of node 2 must be zero: V2 V1 V2 V2 Vb 0 RC RD RE (Applying KCL in this form does not imply that the actual branch currents all are directed out of either node. Indeed, the current in branch 1 2 is necessarily directed out of one node and into the other.) Putting the two equations for V1 and V2 in matrix form,

CHAP. 4]

Topography can be scaled to any size making it very simple to include. It can be defined by angle of slope. The problem with angle of slope, though, is that it can be more a function of the friction of the material and the tread shape of whatever is in ground contact, than a function of the geometry of the mobility system. There are some geometries that are easier to control on steep slopes, and there are some walkers, climbers

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Note the symmetry of the coe cient matrix. The 1,1-element contains the sum of the reciprocals of all resistances connected to note 1; the 2,2-element contains the sum of the reciprocals of all resistances connected to node 2. The 1,2- and 2,1-elements are each equal to the negative of the sum of the reciprocals of the resistances of all branches joining nodes 1 and 2. (There is just one such branch in the present circuit.) On the right-hand side, the current matrix contains Va =RA and Vb =RE , the driving currents. Both these terms are taken positive because they both drive a current into a node. Further discussion of the elements in the matrix representation of the node voltage equations is given in 9, where the networks are treated in the sinusoidal steady state.

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