UNDERACTUATED ROBOTICS
Algorithms for Walking, Running, Swimming, Flying, and Manipulation
Russ Tedrake
© Russ Tedrake, 2018
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Note: These are working notes used for a course being taught at MIT. They will be
updated throughout the Spring 2018 semester.
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CHAPTER 4
Walking and Running
Practical legged locomotion is one of the fundamental unsolved problems in
robotics. Many challenges are in mechanical design - a walking robot must carry all
of its actuators and power, making it difficult to carry ideal force/torque -
controlled actuators. But many of the unsolved problems are because walking
robots are underactuated control systems.
In this chapter we'll introduce some of the simple models of walking and robots,
the control problems that result, and a very brief summary of some of the control
solutions described in the literature. Compared to the robots that we have studied
so far, our investigations of legged locomotion will require additional tools for
thinking about limit cycle dynamics and dealing with impacts.
4.1 WHY IS WALKING SO HARD?
4.2 STATE OF THE ART
4.3 THE BALLISTIC WALKER
One of the earliest models of walking was proposed by McMahon[51], who argued
that humans use a mostly ballistic (passive) gait. COM trajectory looks like a
pendulum (roughly walking by vaulting). EMG activity in stance legs is high, but
EMG in swing leg is very low, except for very beginning and end of swing.
Proposed a three-link "ballistic walker" model, which models a single swing phase
(but not transitions to the next swing nor stability). Interestingly, in recent years the
field has developed a considerably deeper appreciation for the role of compliance
during walking; simple walking-by-vaulting models are starting to fall out of favor.
McGeer[52] followed up with a series of walking machines, called "passive dynamic
walkers". The walking machine by Collins and Ruina[53] is the most impressive
passive walker to date.
4.4 THE RIMLESS WHEEL
Figure 4.1 - The rimless wheel. The orientation of the stance leg, , is
measured clockwise from the vertical axis.
The most elementary model of passive dynamic walking, first used in the context of
walking by [54], is the rimless wheel. This simplified system has rigid legs and only
a point mass at the hip as illustrated in the figure above. To further simplify the
analysis, we make the following modeling assumptions:
θ
Underactuated Robotics
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