Stability analysis and control for bipedal locomotion using energy methods

In this thesis, we investigate the stability of limit cycles of passive dynamic walking. The formation process of the limit cycles is approached from the view of energy interaction. We introduce for the first time the notion of the energy portrait analysis originated from the phase portrait. The energy plane is spanned by the total energy of the system and its derivative, and different energy trajectories represent the energy portrait in the plane. One of the advantages of this method is that the stability of the limit cycles can be easily shown in a 2D plane regardless of the dimension of the system. The energy portrait of passive dynamic walking reveals that the limit cycles are formed by the interaction between energy loss and energy gain during each cycle, and they are equal at equilibria in the energy plane. In addition, the energy portrait is exploited to examine the existence of semi-passive limit cycles generated using the energy supply only at the take-off phase. It is shown that the energy interaction at the ground contact compensates for the energy supply, which makes the total energy invariant yielding limit cycles. This result means that new limit cycles can be generated according to the energy supply without changing the ground slope, and level ground walking, whose energy gain at the contact phase is always zero, can be achieved without actuation during the swing phase. We design multiple switching controllers by virtue of this property to increase the basin of attraction. Multiple limit cycles are linearized using the Poincare map method, and the feedback gains are computed taking into account the robustness and actuator saturation. Once a trajectory diverges from a basin of attraction, we switch the current controller to one that includes the trajectory in its basin of attraction. Numerical simulations confirm that a set of limit cycles can be used to increase the basin of attraction further by switching the controllers one after another. To enhance our knowledge of the limit cycles, we performed sophisticated simulations and found all stable and unstable limit cycles from the various ground slopes not only for the symmetric legs but also for the unequal legs that cause gait asymmetries. As a result, we present a novel classification of the passive limit cycles showing six distinct groups that are consecutive and cyclical

Metastable legged-robot locomotion

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2008.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 195-215).A variety of impressive approaches to legged locomotion exist; however, the science of legged robotics is still far from demonstrating a solution which performs with a level of flexibility, reliability and careful foot placement that would enable practical locomotion on the variety of rough and intermittent terrain humans negotiate with ease on a regular basis. In this thesis, we strive toward this particular goal by developing a methodology for designing control algorithms for moving a legged robot across such terrain in a qualitatively satisfying manner, without falling down very often. We feel the definition of a meaningful metric for legged locomotion is a useful goal in and of itself. Specifically, the mean first-passage time (MFPT), also called the mean time to failure (MTTF), is an intuitively practical cost function to optimize for a legged robot, and we present the reader with a systematic, mathematical process for obtaining estimates of this MFPT metric. Of particular significance, our models of walking on stochastically rough terrain generally result in dynamics with a fast mixing time, where initial conditions are largely "forgotten" within 1 to 3 steps. Additionally, we can often find a near-optimal solution for motion planning using only a short time-horizon look-ahead. Although we openly recognize that there are important classes of optimization problems for which long-term planning is required to avoid "running into a dead end" (or off of a cliff!), we demonstrate that many classes of rough terrain can in fact be successfully negotiated with a surprisingly high level of long-term reliability by selecting the short-sighted motion with the greatest probability of success. The methods used throughout have direct relevance to machine learning, providing a physics-based approach to reduce state space dimensionality and mathematical tools to obtain a scalar metric quantifying performance of the resulting reduced-order system.by Katie Byl.Ph.D

Energetics and Passive Dynamics of Quadruped Robot Planar Running Gaits

Quadruped robots find application in military for load carrying over uneven terrain, humanitarian de-mining, and search and rescue missions. The energy required for quadruped robot locomotion needs to be supplied from on-board energy source which can be either electrical batteries or fuels such as gasolene/diesel. The range and duration of missions very much depend on the amount of energy carried, which is highly limited. Hence, energy efficiency is of paramount importance in building quadruped robots. Study of energy efficiency in quadruped robots not only helps in efficient design of quadruped robots, but also helps understand the biomechanics of quadrupedal animals. This thesis focuses on the energy efficiency of planar running gaits and presents: (a) derivation of cost of transport expressions for trot and bounding gaits, (b) advantages of articulated torso over rigid torso for quadruped robot, (c) symmetry based control laws for passive dynamic bounding and design for inherent stability, and (d) effect of asymmetry in zero-energy bounding gaits

Using MapReduce Streaming for Distributed Life Simulation on the Cloud

Distributed software simulations are indispensable in the study of large-scale life models but often require the use of technically complex lower-level distributed computing frameworks, such as MPI. We propose to overcome the complexity challenge by applying the emerging MapReduce (MR) model to distributed life simulations and by running such simulations on the cloud. Technically, we design optimized MR streaming algorithms for discrete and continuous versions of Conway’s life according to a general MR streaming pattern. We chose life because it is simple enough as a testbed for MR’s applicability to a-life simulations and general enough to make our results applicable to various lattice-based a-life models. We implement and empirically evaluate our algorithms’ performance on Amazon’s Elastic MR cloud. Our experiments demonstrate that a single MR optimization technique called strip partitioning can reduce the execution time of continuous life simulations by 64%. To the best of our knowledge, we are the first to propose and evaluate MR streaming algorithms for lattice-based simulations. Our algorithms can serve as prototypes in the development of novel MR simulation algorithms for large-scale lattice-based a-life models.https://digitalcommons.chapman.edu/scs_books/1014/thumbnail.jp