Bipeds on a Budget
Or, “How to make a two-legged walker with few degrees of freedom.”
One thing I’ve always been fascinated by is making walking biped robots with limited degrees of freedom (DOF). Each degree of freedom requires a servo, and servos strong enough for a biped walker tend to be expensive. In addition, more servos means more weight, and more weight requires stronger servos; this explains why any good humanoid robot (with 16 DOF or more) is likely to cost $1000 or more. For people new to the hobby, this is likely to be too big an investment to make right away. It’s so much better to start smaller, and work out all the command & control issues while feeding one’s growing addiction with a lower-cost robot.
This leads to the natural question: how many servos do you really need to make a walking biped? In this blog post, I’ll attempt to answer that question with a quick survey of low-DOF biped robots.
With a single servo, you basically can’t make anything better than a wind-up robot toy. These essentially have overlapping feet, accomplish via long prongs that stick out from the toe and heel of each foot, towards the other foot. As a result, the robot’s center of gravity is always over the support polygon (the area on the floor enclosed by the supporting foot), and it can easily stand on one foot or walk without falling over, using only a single motor to cycle both feet. But overlapping feet is cheating, in my book, and even with that cheat, such a robot can’t turn; it can only walk forward and backward. ‘Nuff said.
You might expect that two servos isn’t enough for a true biped either. But you’d be wrong. In 1998, hobby roboticist David Buckley developed a two-servo robot called BigFoot. Bigfoot uses one servo to drive the feet alternately back and forth, using parallel linkages to keep the feet parallel with the floor. Then it uses a second servo, with another linkage to each foot, to tilt both feet side to side. This allows the robot to shift its weight from one foot to the other — a task made easier by purposely designing the robot to be tall, with a high center of gravity (COG), so that a smaller tilt angle results in a big horizontal shift. The robot can walk stably, and turn by skidding its feet. This ingenious design has since been commercialized as the Parallax Toddler. David has since made other variations of this design, such as Bambino.
Three-servo bipeds are pretty rare. One example is “Dead Duck Walking” by Frits Lyneborg. This uses one servo to tilt both feet sideways, one to twist them in and out, and a third to shift a weight (the batteries) side to side to aid with balance.
Though I haven’t seen it done yet, another idea for a 3-servo biped would involve 1-DOF legs that can step forward or backward, plus a counterbalance servo to shift the COG over the supporting foot. For 1-DOF legs, see this 2008 paper by Liang, Ceccarelli, & Takeda. Or, consider using something like a Klann linkage. In either of these cases, you have the problem that the lower leg does not maintain a constant angle with respect to the ground, so you can’t just bolt on a foot; you’d need to add some sort of parallel linkage to the leg to keep the foot level. But it just might work.
David Buckley, the mechanical wizard behind BigFoot, has written a wonderful treatise on minimalist biped walkers. In it, he describes the “Aesir” series of 4-servo bipeds, developed in 2002. The first was Loki, which uses a servo at each hip to yaw the leg around the vertical axis; and another in each ankle to tilt (roll) the foot sideways. Using the ankle servos, Loki can shift its weight onto one foot, then use both hip pivots to move the other foot forward or backward to take a step. Thanks to the hip pivots, it’s also able to turn without skidding.
The Loki design has since been copied widely. Most famous is the LynxMotion Brat Jr., which many people have built in various forms (including my own 4S-1). The Hovis Lite kit includes plans for a Loki-style biped, and similar beasts have been built using Bioloid parts. Thingiverse even has a couple of printable part kits for Loki derivatives, including a cute one called “Arduped.”
David went on to make another robot called Frea, with a different servo arrangement: the hip servos swing the legs out sideways, and the ankle servos yaw around the vertical axis. With this arrangement, Frea is able to stand up from any starting position. However, to make it work, David had to use overlapping feet — which is still cheating in my book, but an impressive robot nonetheless. (See also Thor, which uses essentially the same design, but has a cool reverse-knee mech look.)
Are there other arrangements of four servos that can walk well? One can easily imagine use parallel-linkage legs, like in BigFoot, but with an independent servo moving each leg forward and back. This, combined with the ankle tilt servos, would enable walking similar to BigFoot’s, but more versatile. (Now that I think of it, I’ve pretty much described TecFoot minus the fifth servo — see below.) However, it’s still not as versatile as the Loki design, since it can’t pivot its feet to turn. If you have any other ideas (or references) for 4-servo walkers, please post ‘em in the comments below.
Despite the risk of sounding like a David Buckley cheerleader, I have to turn to him yet again for a good example of a 5-servo walker. This is TecFoot, a tall walker that uses two servos per leg, to independently tilt at the ankle, and swing forward/back; plus one more servo which splays the feet inward or outward together. That’s accomplished by mounting each leg on a hinge, and using a servo in the center of the body to move these hinges in or out at the hip.
As with all of David’s designs, this is a very clever and efficient use of servos, based upon the recognition that you don’t much care about the orientation of the foot that’s in the air; only the supporting foot matters. (And when standing on both feet, there’s not much point in pivoting them at all.)
By this point, we’re stretching the definition of “minimal” quite a bit. Making a biped with 3 DOF per leg is fairly easy, and is exemplified by the LynxMotion BRAT. This design uses hip servos to swing the leg back and forth; knee servos to bend like knees do; and ankle servos to tilt the feet sideways. So, using the ankle servos, the robot can shift its weight onto one foot, then use the hip and knee to take a nice big step with the other one.
Because this design lacks any rotation about the vertical axis, it has to turn by shuffling, much like the 2-servo BigFoot. There are undoubtedly many other 6-servo configurations that would also work. Considering just the rotation axis, there are 3^3 = 27 different arrangements of the servos for each leg — and that’s not including details of the placement, nor variations that use linkages. So, that might have to be a topic for another post.
What do you think? Have I missed any important arrangements for low-DOF bipeds? What’s your favorite design? Weigh in with your thoughts in the comment area below.