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My research interests are in robotics, control systems, dynamics, and biomechanics, particlarly topics related to robot and human walking. My research advisor is Professor Mark W. Spong.

If you are a student at the University of Illinois and find this research area interesting, here are some excellent undergraduate courses in robotics, as well as information about attending the meetings of my two research groups (one for robot locomotion and one for human locomotion).

Publications

Walking Robots

Legged locomotion has fascinated researchers for years. Wheeled machines, while highly efficient, are limited to smooth terrain. Legged devices, on the other hand, hold the prospect of navigating irregular terrain. The study of bipedal locomotion draws additional interest because of its immediate application to human walking and the development of lower body prosthetics. Until the late 1980s, the state of the art in bipedal robotics involved specifying the motion of each joint in a robot’s legs. The task then became one of designing controllers to produce the preplanned motion. This approach, though it yielded human-like gaits, was disappointingly energy inefficient. The Honda ASIMO robot is an example of this classical approach. While it is interesting to watch ASIMO in action, it is estimated that ASIMO’s specific cost of transport ( energy used / (weight × distance traveled) ) is some 32 times greater than that of a typical human [1].

In 1984, McMahon [2] noted the similarities between human walking and a certain bipedal child’s toy shown below. When set on a ramp and given a push, the toy would waddle side to side and “walk” its way down the ramp. Remarkable about the toy is the absence of an external source of energy; it was driven by gravity. The toy’s simple, uncontrolled gait hinted that locomotion is fundamental to a system of links and joints and needs no external energy or planning to bring it about. Within 15 years, multiple robotics laboratories across North America and Europe were investigating this phenomenon.



An unpowered toy that will “walk” down a ramp.

Passive Dynamic Walking

In 1990, McGeer [3] demonstrated unpowered bipedal locomotion with a simple robot similar to the one shown below. When placed on a ramp and given a proper initial push, the biped would walk down the ramp. With each step the walker gained energy from the change in potential on the decline, and the ground impact at the end of each step dissipated the extra energy. With the right combination of initial conditions and ramp angle, each successive step exactly matched the previous step and a stable gait emerged.



McGeer's first unpowered walker.

This remarkable gait became known as passive dynamic walking. The term passive comes from the fact that no external source other than gravity provides power for each step. Dynamic is used to classify the type of stability associated with bipedal walking. For a quadruped, the center of mass always remains above a support region defined by the three feet that are on the ground at any given time; this is known as statically stable walking. In human bipedal walking, however, the ground projection of the center of mass is constantly making excursions outside the support area defined by the one foot on the ground. Stability for such a gait requires that it be constantly in motion, continually interrupting the falling motion of the body with a successive step. This is called dynamic stability. Since dynamically stable gait makes possible faster walking speeds, the literature commonly focuses on is required for any sustainable bipedal gait, it is common in the literature to simply refer to passive walking.

Walking with Knees, Arms, and Active Control

McGeer also demonstrated passive walking for a biped with knees [4,5], pictured in the figure below. For both of McGeer’s walkers, all motion was restricted to the sagittal (profile) plane of the robot. Since lateral (side-to-side) motion was eliminated by having the legs swing in pairs like crutches, McGeer’s work demonstrated passive walking only in two dimensions. In 2001, Collins, Wisse, and Ruina [6] successfully stabilized lateral motion by cleverly modifying a 2D passive walker design. They added wide, round feet and arms whose motion was coupled to the leg on the opposite side. Their walker, also shown below, was the first to demonstrate passive walking in three dimensions.


Two-dimensional passive dynamic walkers with knees:
(left) McGeer’s walker and (right) a similar walker from Ruina’s lab at Cornell.


A 3D passive dynamic walker with knees and arms built by Collins, Wisse, and Ruina.

Using the lessons learned from the passive walkers, researchers began building highly efficient biped robots capable of walking not only on ramps, but on flat surfaces as well. These devices required active control to reproduce the effect of gravity on shallow declines that generated unpowered gait. A number of actuated robots based on passive dynamic principles have been built at Cornell University, Delft Technical University, and the Massachusetts Institute of Technology [1]. One of these is a biped that essentially reproduces 2D passive dynamic gait on level ground [7]. Another biped reproduces 3D passive dynamic gait on level ground [1]. Both of the bipeds are shown below.



Walkers with active control based on passive dynamic principles:
(left) Wisse’s 2D walker with knees and (right) Collin’s 3D walker with knees and arms.

Comparison to Human Walking

A study of electromyography (EMG) data collected from walking humans reveals that muscles in our legs are relatively inactive during the swing phase of walking [8]. This seems to imply that human walking is largely a passive motion, indicating a strong correlation with the passive robots. All of the robots based on passive walking demonstrate promising energy efficiency comparable to human walking. For example, the specific cost of transport of the biped shown on the right above is roughly equivalent to that of humans [1].

Analysis and Control

Much has been published about passive dynamic walking since McGeer’s pioneering work in the late 1980s and early 1990s. McGeer’s [3] analysis of his biped without knees was based around a linearized mathematical model of his walking robot. In the mid 1990s, Goswami et al. [9–11] published results based on the full nonlinear model of such a biped. They reported findings on the stability of the repetitive walking pattern which, in the language of nonlinear control, is called a limit cycle [9,10,12]. In 2001, Yamakita and Asano [13] presented the full nonlinear model of the biped with knees and its limit cycle. Goswami et al. [10,11] also showed that increasing the slope of the surface on which the passive biped walks leads to asymmetric gaits and eventually chaotic behavior. In addition, in [10] Goswami et al. proposed a method of control based on the energy of a passive limit cycle that allows an actuated biped to walk on level ground or up an incline.

In 1999, Spong [14] followed up Goswami’s work with a control law that renders the passive limit cycle slope invariant, enabling a biped to walk on any specified slope. Spong and Bullo [15] showed that this control law would work for the limit cycle of any passive dynamic robot. Spong and Bhatia [16,17] presented another energy based control law to better handle disturbances. Under this control law, a biped can return to its limit cycle from larger perturbations (the basin of attraction is broadened) and the rate of convergence to the limit cycle is increased.

The Next "Steps"

The field of robotics is just over fifty years old; the study of passive-dynamic walking has been in progress for just fifteen years. There are many open problems to be considered, many opportunities for interested researchers to explore human and machine walking and advance the state of the art in walking robots and prostehtic and orthotic devices.

References

The text and images on this page are taken directly from Chapter 1 of my thesis. You can look up the literature mentioned on this page in the References section of the pdf document.