Robert D. Gregg, IV
University of Illinois at Urbana-Champaign
Current Research
Background on Bipedal Walking Robots
The step-level mechanics and high-level motion planning of humanoid walking have been active areas of research over the past decades. Many have studied bipedal locomotion as a means to more intelligent robotic devices for rehabilitation, prosthesis, and assisted walking. The incredible efficiency of bipedalism, which allows humans to outwalk quadrupeds over long distances, also motivates its use on locomotive mechanisms. In fact, researchers have demonstrated "passive dynamic" walking down shallow slopes for simple planar biped models without any actuation whatsoever (cf. McGeer 1990).
In order for robots to accurately mimick human walking, they must reproduce three important characteristics. Humanoid walking is:
In this energy-efficient form of locomotion, known as dynamic walking, each step cycle involves a gravity-powered pendular fall towards the ground, until foot impact transfers this natural falling motion to the other leg. In terms of a walker's joint trajectories, this produces attractive periodic orbits called limit cycles. Hobbelen and Wisse (2007) offer a useful definition:
Limit cycle [i.e., dynamic] walking is a nominally periodic sequence of steps that is stable as a whole but not locally stable at every instant in time.
Many sophisticated humanoid robots, such as HRP-2 and Honda ASIMO, have demonstrated robotic bipedal locomotion. However, their motion is constrained by quasi-static equilibrium conditions related to the Zero Moment Point (ZMP). This produces unnatural shuffling motion that is not dynamic, and is up to an order of magnitude less efficient than dynamic walkers in terms of energy consumed per unit weight per unit distance (cf. Kuo 2007, Collins and Ruina 2005).
However, dynamic walking studies, typically limited to simple sagittal-plane models, have not sufficiently addressed the other two traits of humanoid locomotion. Arguably, this is because traditional control and analysis techniques become impractical when considering the high-order limit cycles of 3-D walking robots, which have complex dynamics with highly coupled modes and planes-of-motion.
Controlled Geometric Reduction
This motivates our research in geometric methods for reducing dynamics into lower-dimensional control problems. In particular, we are developing the method of controlled geometric reduction, which unifies symmetry-based reduction, symmetry-breaking stabilization, and passivity-based control.We discovered a geometric property of general serial-chain robots termed recursive cyclicity, showing that robots have innate and extensive symmetries that can be exploited (IJRR 09). We consequently introduced the Subrobot Theorem, by which we decompose the control of any serial-chain robot based on lower-dimensional subsystems. We have generalized this result to branched chains, such as bipeds with torsos and articulated arms (CDC 09). In the robotic walking context, this simplifies the search for full-order limit cycles and expands the class of completely 3-D robots that can achieve pseudo-passive dynamic walking.
Consequently, we have designed reduction-based control laws to achieve the first theoretical results in directional 3-D dynamic bipedal walking (ACC 08). We show straight-ahead walking gaits that correspond to stable 2-step periodic trajectories, involving natural side-to-side lateral and axial swaying motions induced by the robot's hip. This nicely resembles the three discussed traits of humanoid walking.
Motion Planning by Gait Primitives
We have also shown that controlled reduction induces periodic turning gaits from constant-curvature steering (IROS 09, CDC 09). These gaits naturally lean into the turn to compensate for centripetal forces, resulting in stable turning motion. These different types of dynamic walking gaits serve as a set of motion primitives that enable locomotion planning on dynamic bipeds in the same way possible with less efficient ZMP bipeds (Submitted ICRA 10). Future work will detail kinodynamic motion planning algorithms for planning stable dynamic walking paths.Simulation Movies:
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Previous Work
Reduced-Order Bipedal Walking
CHESS Bipedal Walking GroupCenter for Hybrid and Embedded Software Systems
Department of Electrical Engineering and Computer Sciences
University of California, Berkeley
Advisers: Dr. Aaron Ames and Prof. Shankar Sastry
Autonomous Mechatronic Racing
Mechatronics Design LaboratoryDepartment of Electrical Engineering and Computer Sciences
University of California, Berkeley
Adviser: Prof. Ron Fearing
This was a team design project with application of theoretical principles in EE/CS to mechatronic systems with sensors, actuators and intelligence. We built a competitive 1/10-scale racing vehicle to autonomously follow an unknown racecourse using power electronics, filtering/signal processing, control theory, electromechanics, microcontrollers, and real-time embedded software. Our vehicle won 1st place at the intercollegiate 2006 NATCAR competition, setting the all-time average speed record.
Team 9 (Rick Mann, John Breneman, Robert Gregg): NATCAR 2006 1st Place Finishers
NATCAR Movies: