Robert D. Gregg, IV
University of Illinois at Urbana-Champaign
Project Descriptions:
3D Bipedal WalkingSynchronizing Gaits
Previous Work
Control and Planning of 3D Bipedal Dynamic Walking
Background
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 mimick human walking, we suggest three important characteristics that must be reproduced. Human-like walking gaits are:
In this energy-efficient form of locomotion, 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 complex 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 identified a geometric property of serial kinematic chains termed recursive cyclicity, showing innate and extensive symmetries that can be exploited to decompose robot control into on lower-dimensional subsystems (IJRR 09). We have generalized this result to branched kinematic 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 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.
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Media Coverage:
Synchronization of Walking Gaits
In collaboration with Professor Prashant Mehta and undergraduate Adam Tilton, we are investigating efficient means of synchronizing asymptotically stable walking gaits, particularly applied to passive dynamic walkers. This project has implications on formations of multi-agent systems as well as CGI animations of human locomotion. A particular area of interest is lower extremity prosthetic control systems, where robotic limbs must be synchronized with the governing motion of the sound human limb.Using passivity-based control tools from Chopra and Spong (2006), we have demonstrated asymptotic synchronization of groups of passive walkers without individually destabilizing gaits, despite the presence of impact discontinuities. We investigate multiple communication topologies, including strategies with discrete-event switching. In order to produce human-like synchronization of walking gaits or hand clapping, future work will involve discrete event-based communication inspired by neural encoding models.
Simulation Movies for Communication Topologies:
(Note: Communication links between joints are illustrated in the phase trajectories)
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
Simulation Movies:
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: