The object of this project is to develop control algorithms for bipedal walking robots using concepts of geometric reduction. Geometric reduction takes advantage of certain symmetry properties in the dynamic equations of bipedal robots and facilitates the computation of lower dimensional models for analysis and control design. The goal is to enable control concepts developed for two-dimensional, or planar, bipeds to be applied to fully three-dimensional bipeds. In this way, the complexity of the control problem for three-dimensional walking robots is greatly reduced. The project will also investigate the effects of asymmetries in leg parameters, such as leg length and leg mass, on the existence and properties of passive gaits. Preliminary investigations indicate that asymmetry in leg parameters, such as leg mass, results in qualitative changes in gait, such as period-doubling bifurcations and chaotic motion. Deliverables from this research include new control algorithms, new simulation models and graphical simulation tools for visualization of simulation data.
The practical application of this research is in the design of walking robots that have improved performance capabilities over existing machines. Current walking robots have limited range due to poor energy utilization and are limited in their ability to navigate uneven terrain. More practical and more efficient walking machines will result once the full power of available theoretical tools is brought to bear on the analysis and design questions in this project. The tools developed in this project will also contribute to a better understanding of human locomotion, which will result in applications in biomechanics and biomedicine, such as the design of improved prosthetic devices, the development of falls prevention programs for the elderly, and rehabilitation techniques. The study of bipeds with parameter asymmetry is motivated by the desire to understand the effect of asymmetry of human gait on walking stability, performance, and gait disorders. Our research results will also be used to create demonstrations and presentations for middle school and high school students to be used as recruiting tools. Our past experience has shown that robotics is an excellent vehicle to attract and retain students in engineering.
This project is to investigate improved strategies for controlling bipedal walking robots and generating improved walking gaits. Based on the idea of passive dynamic walking, we have developed provably correct algorithms for full three-dimensional walking. Previous work was mainly limited to two dimensional walking in the saggital plane. We also investigated the existence and stability of passive limit cycles in bipedal robots with asymetries, for example when the masses of the legs are different. Such work can have applications to walking with one normal and one prosthetic leg, for example. It can also have applications for rehabilitation of stroke victims and individuals with other medical conditions. We showed the existence of bifurcations in gaits leading to chaotic limit cycles as a function of the ratio of leg masses. Broader impacts of this work include the design and control of improved walking robots, a better understanding of human locomotion, and improved methods for rehabilitation and design and control of prosthetic limbs. We also supported several undergraduate students through an REU supplement to this grant. Publications arising from this grant include: Leonid Freidovich, Anton Shiriaev, Mark W. Spong, "Controlled Invariants and Trajectory Planning for Underactuated Mechanical Systems," IEEE Transactions on Automatic Control, submitted, 2012. Jae-Sung Moon, Dusan Stipanovic, Mark W. Spong, "Generation and Stabilization of Passive Limit Cycles for Level Ground Walking and Speed Regulation," IEEE Transactions on Robotics, submitted, 2012. R. D. Gregg and A. K. Tilton and S. Candido and T. Bretl and M. W. Spong, Control and Planning of 3D Dynamic Walking with Asymptotically Stable Gait Primitives, IEEE Transactions on Robotics, accepted for publication. to appear, 2012. Jae-Sung Moon and Mark W. Spong, Classi cation of Periodic and Chaotic Passive Limit Cycles for a Compass-Gait Biped with Gait Asymmetries," Robotica, Vol. 29, pp. 967-974, 2011. Leonid B. Freidovich, Uwe Mettin, Anton S. Shiriaev, Mark W. Spong, A Passive 2DOF Walker: a Hunt for Gaits using Virtual Holonomic Constraints," IEEE Transactions on Robotics, Volume: 25, Issue: 5, pp. 1202-1208, 2009. Robert D. Gregg and Mark W. Spong, "Reduction-based Control of Three-Dimensional Bipedal Walking Robots," Int. J. Robotics Research, Vol. 29, No. 6, pp. 680-702, May, 2010. Anton Shiriaev, Leonid Freidovich, Mark W. Spong, "A Remark on Controlled Lagrangian Approach for Completely Integrable Mechanical Systems," 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Bertinoro, Italy, August 29-31, 2012. Joohyung Kim, Chong-Ho Choi and Mark W. Spong, "Passive Dynamic Walking with Knee and Fixed Flat Feet," International Conference on Control, Automation and Systems (ICCAS) 2012, Jeju, South Korea, October, 17-21, 2012. Robert D. Gregg, Timothy Bretl, and Mark W. Spong, "A Control Theoretic Strategy for Underactuated Human Gait Assistance," IEEE Conference on Decision and Control, Atlanta, GA, December, 2010. Robert D. Gregg, Tim Bretl, and Mark W. Spong, Asymptotically Stable Gait Primitives for Planning Dynamic Bipedal Locomotion in Three Dimensions," IEEE Int. Conference on Robotics and Automation, pp. 1695 - 1702, Anchorage, AL, May, 2010.J ae-Sung Moon and Mark W. Spong, "Bifurcations and Chaos in Passive Walking of a Compass-Gait Biped with Asymmetries," IEEE Int. Conference on Robotics and Automation, pp. 1721 - 1726, Anchorage, AL, May 3-8, 2010.
