Tripawd: the three-legged robot dog.

The research question

Tripawd is a three-legged robot dog, developed at Carnegie Mellon in the course 24-775, Robot Design and Experimentation. Our team wanted to explore a question about the gait of a three-legged dog: how optimally does a three-legged dog's natural gait perform in terms of cost of travel, compared to a gait found through trajectory optimization?

Stated formally, the question we set out to answer was whether applying the walking gait of an amputee three-legged dog to a quadruped robot missing the corresponding leg would optimize the robot's cost of travel.

Biological inspiration and control

Our biological inspiration was the motion of an amputee three-legged dog. When a dog loses a leg, it adapts into a natural gait that keeps it stable and mobile, and we wanted to know whether that adapted gait is actually efficient, or just a local minimum that biology settled on.

We drew on prior work in quadruped control. One useful design principle is the gravitationally decoupled actuator (GDA), which addresses energy efficiency, design, and adaptive gait control in quadruped walking vehicles. We also looked at model-reference adaptive control (MRAC), which adapts a control law through parameter changes against a predefined reference plant. The catch is that losing a leg changes the plant model completely, so MRAC has no valid reference to adapt from and can't produce an efficient three-legged gait on its own. That limitation is part of why we turned to trajectory optimization to design the optimized gait.

What we built

A three-legged platform driven by Dynamixel servos, with each leg a simple multi-link chain. The hard part of a tripod isn't the legs, it's that with only three contact points the robot is always one lifted leg away from being statically unstable. Unlike a quadruped, it can't just keep three feet on the ground and swing the fourth; every step has to actively manage where the center of mass sits relative to the remaining support. That constraint drove most of the mechanical layout and gait design.

The experiment

We compared two gaits on the same hardware. The natural gait was hand-designed to mimic how a real three-legged dog moves, the pattern biology settles into. The optimized gait came out of a trajectory optimization that minimized energy use subject to the stability constraint. Cost of transport, the energy spent per unit distance per unit weight, was the common yardstick, so the two could be compared directly on the physical robot.

Results

The demonstration video above walks through the project and our results in full: how the robot was built, how each gait was generated, and how the two compared on cost of transport.

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