Sandin P.E. Robot mechanisms and mechanical devices illustrated

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204 Chapter 7 Walkers

Figure 7-1 One-DOF leg for

frame walkers

Figure 7-2 Two-DOF leg using

linear actuators

Chapter 7 Walkers 205

Rotary actuators (Figure 7-4) are the most elegant, but make the joints

large. The cable driven layout (Figure 7-5) takes up the least volume and

has no exposed actuators. Both of these methods are common, mostly

because they use motors in a simple configuration, rather than linear

actuators. Their biggest drawback is that they need to be big to get

enough power to be useful. iRobot’s Genghis robot used two hobby ser-

vos bolted together, acting as rotary actuators, to get a very effective two-

axis hip joint. This robot, and several others like it, use simple straight

legs. These simple walker layouts are useful preliminary tools for those

interested in studying six-legged walking robots.

To turn the two-DOF linear actuator layout into a three-DOF, a uni-

versal joint can be added at the hip joint. This is controlled with an actu-

ator attached horizontally to the chassis. Figure 7-6 shows a simple

design for this universal hip joint. The order of the joints (swing first,

then raise; or raise first, then swing) makes a big difference in how the

foot location is controlled and should be carefully thought out and proto-

typed before building the real parts.

The three-DOF rotary actuator leg (Figure 7-7) adds a knee joint to

the Genghis layout for improved dexterity and mobility. There are many

varieties of this layout that change the various lengths of the segments

Figure 7-3 Two-DOF leg using

linear actuators with

chassis-mounted knee actuator

206 Chapter 7 Walkers

Figure 7-4 Two-DOF leg using

rotary actuators

Figure 7-5 Two-DOF leg using

cable driven actuators

Chapter 7 Walkers 207

Figure 7-6 Three-DOF leg using

linear actuators

Figure 7-7 Three-DOF leg using

rotary actuators

208 Chapter 7 Walkers

and the relative location of each actuator. It is quite difficult to drive a

two-DOF hip joint with cables, but it can be done. The general layout

would look much like what is shown in Figure 7-7.

WALKING TECHNIQUES

Statically-stable walkers are easier to implement than dynamically-sta-

ble walkers. A method used to group statically-stable walkers is the tech-

nique used to move the legs. There are three useful sub groups: wave

walking, independent leg walking, and frame walking. Wave walking is

what animals with many legs use, like millipedes. Independent leg walk-

ing is used by just about every four, six, and eight-leg walker, although

some simplify things by moving their legs in groups for certain speeds or

motions. Frame walking exists in nature in the form of an inchworm, and

is the simplest of the three, but to have high mobility still requires many

actuators. As we shall see, frame walking can be a very effective mobil-

ity method for a mobile robot.

Wave Walking

Centipedes and millipedes use a walking technique that must be men-

tioned, although it is simple in concept, for walking robots, it is less effi-

cient than other methods. The robot lifts its rear-most set of legs and

swings them forward and sets them down, then the next set of legs is

moved similarly. When the front-most set of legs is moved, the whole

robot chassis is moved forward relative to the legs. The process can be

smoothed out some by averaging the position of the body as each set of

legs moves forward. This technique can be used with six- or more-legged

robots, but is not very common in robots because of the large numbers of

joints and actuators.

Independent Leg Walking

Virtually all other legged animals in nature that don’t use wave walking

can control each leg independently. Some animals are better than others,

but the ability is there. Figures 7-8 and 7-9 show four- and six-legged

walkers with three rotary-actuated joints in each leg. An eight-leg layout

would have no less than 24 actuators. The four- and six-legged versions

Chapter 7 Walkers 209

Figure 7-8 Independent leg

walker, four legs, twelve DOF

Figure 7-9 Independent leg

walker, six legs, eighteen DOF

210 Chapter 7 Walkers

theoretically have very high mobility. Many research robots have been

built that use four or six legs and are impressively agile, if very slow.

Although it would seem impossible to build a two-legged statically-

stable robot, there is a trick that toys and some research robots use that

gives the robot the appearance of being dynamically stable when they are

actually statically stable. The trick is to have feet that are large enough to

hold the robot upright on one foot without requiring the foot to be in

exactly the right place. In effect, foot size reduces the required accuracy

of foot placement so that the foot can be placed anywhere it can reach

and the robot will not fall over.

The wide feet must also prevent tipping over sideways and are so wide

that they overlap each other and must be carefully shaped and controlled

so they don’t step on each other. Two-legged walking, with oversized

and overlapping feet, is simply picking up the back foot, bringing it for-

ward, and putting it down. The hip joints require a second DOF in addi-

tion to swinging fore and aft, to allow rotation for turning. Each leg must

have at least three DOF, and usually requires four. The layout shown in

Figure 7-10 can only walk in a straight line because it lacks the hip rota-

tion joint. Notice that even with only two legs and no ability to turn, this

layout requires six actuators to control its six degrees of freedom.

This layout provides a good educational tool to learn about walking.

Although in the final implementation it may have eight DOF and its

Figure 7-10 Extra wide feet

provide two-legged stability

Chapter 7 Walkers 211

knees bend backwards, it is familiar to the designer. One leg at a time can

be built, tested, and debugged and then both attached to a simple plate

for a chassis.

Frame Walking

The third general technique for walking with a legged robot is frame

walking. Frame walking relies on the robot having two major sections,

each with their own set of legs, both sections statically stable. Walking is

accomplished by raising the legs of one frame, traversing that frame for-

ward relative to the frame whose legs are still on the ground, and then

setting the legs down. The other frame’s legs are then raised and tra-

versed forward.

The coupling between the two frames usually has a second rotating

DOF to facilitate turning, rather than by adding a rotation in each leg.

Figure 7-11 shows a mechanism for traversing and turning the two parts

of the body. In nature, an inchworm uses a form of frame walking. The

two frames are the front and back sections of the worm. The coupling is

the leg-less section in between. In the case of the inchworm, the coupling

has many degrees of freedom, but two is all that is required if the legs

each have their own ability to move up and down. Unfortunately for

robot designers, the inchworm also has the ability to grasp with its claw-

Figure 7-11 Mechanism for

frame traversing and rotating

212 Chapter 7 Walkers

Figure 7-12 Traversing/rotating

frame eight-leg frame walker with

single-DOF legs

Figure 7-13 Eight-leg frame

walker with two-DOF legs

Chapter 7 Walkers 213

like feet, making it quasi-statically stable. Figure 7-12 shows an imple-

mentation of the traversing/rotating frame with simple one-DOF legs.

This layout has 10 DOF. Figure 7-13 removes the rotating joint, which

forces placing a second joint in each leg to be able to turn. The actuator

count goes up to 17 with this layout. The advantage of having the second

joint in each leg is the ability to place each leg in the most optimum point

to maintain traction and stability. Still, 17 actuators is a lot to control and

maintain.

A six-leg tripod-gait frame walker could, however, have just three

degrees of freedom, all in one joint between the two frames. This joint

would have a linear motion for traversing, a rotary motion for steering,

and a vertical motion to lift one frame and then the other. Mobility would

suffer with such a simple platform because the robot would lack the abil-

ity to stand level on uneven terrain. Perhaps the best is a six-leg tripod-

gait frame walker with one linear DOF in each leg and two in the cou-

pling, bringing the total DOF to eight. Figure 7-14 shows just such a

layout, perhaps the best walking layout to start with if designing a walk-

ing robot.

Figure 7-14 Six-legged

tripod-frame walker with

single-DOF legs