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

Explainable robotics applied to bipedal walking gait development

Explainability is becoming an important topic in artificial intelligence (AI). A well explainable system can increase the trust in the application of that system. The same holds for robotics where the walking gait controller can be some AI system. We will show that a simple and explainable controller that enables an energy efficient walking gait and can handle uneven terrains, can be developed by a well structured design method. The main part of the controller consist of three simple neural networks with 4, 6 and 8 neurons. So, although creating a stable and energy efficient walking gait is a complex problem, it can be generated without some deep neural network or some complex mathematical model

Adaptive motion synthesis and motor invariant theory.

Generating natural-looking motion for virtual characters is a challenging research topic. It becomes even harder when adapting synthesized motion to interact with the environment. Current methods are tedious to use, computationally expensive and fail to capture natural looking features. These difficulties seem to suggest that artificial control techniques are inferior to their natural counterparts. Recent advances in biology research point to a new motor control principle: utilizing the natural dynamics. The interaction of body and environment forms some patterns, which work as primary elements for the motion repertoire: Motion Primitives. These elements serve as templates, tweaked by the neural system to satisfy environmental constraints or motion purposes. Complex motions are synthesized by connecting motion primitives together, just like connecting alphabets to form sentences. Based on such ideas, this thesis proposes a new dynamic motion synthesis method. A key contribution is the insight into dynamic reason behind motion primitives: template motions are stable and energy efficient. When synthesizing motions from templates, valuable properties like stability and efficiency should be perfectly preserved. The mathematical formalization of this idea is the Motor Invariant Theory and the preserved properties are motor invariant In the process of conceptualization, newmathematical tools are introduced to the research topic. The Invariant Theory, especially mathematical concepts of equivalence and symmetry, plays a crucial role. Motion adaptation is mathematically modelled as topological conjugacy: a transformation which maintains the topology and results in an analogous system. The Neural Oscillator and Symmetry Preserving Transformations are proposed for their computational efficiency. Even without reference motion data, this approach produces natural looking motion in real-time. Also the new motor invariant theory might shed light on the long time perception problem in biological research

Design and experimental analysis of legged locomotive robots

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 20-21).In this thesis, I present the design and motion-capture analysis of two previously well-studied dynamic-walking machines, the rimless wheel and the compass gait robot. These robots were the basis for my undergraduate research at the Computer Science/Artificial Intelligence Laboratory (CSAIL) at the Massachusetts Institute of Technology. The rimless wheel is a real-world physical realization built to compare to a long-analyzed model, the simplest example of passive dynamic walking. Despite the seemingly deterministic model, undeniable experimental evidence for unpredictable stochasitic behavior is observed. The compass gait is the second iteration of a previous design by Dr. Fumiya Iida in my laboratory. Both machines are among the most fundamental walking models, and are important for developing energy-efficient dynamic walkers.by Timothy J. Villabona.S.B

Effect of the Dynamics of a Horizontally Wobbling Mass on Biped Walking Performance

We have developed biped robots with a passive dynamic walking mechanism. This study proposes a compass model with a wobbling mass connected to the upper body and oscillating in the horizontal direction to clarify the influence of the horizontal dynamics of the upper body on bipedal walking. The limit cycles of the model were numerically searched, and their stability and energy efficiency was investigated. Several qualitatively different limit cycles were obtained depending mainly on the spring constant that supports the wobbling mass. Specific types of solutions decreased the stability while reducing the risk of accidental falling and improving the energy efficiency. The obtained results were attributed to the wobbling mass moving in the opposite direction to the upper body, thereby preventing large changes in acceleration and deceleration while walking. The relationship between the locomotion of the proposed model and the actual biped robot and human gaits was investigated.Comment: 6 pages, 8 figures, accepted to IEEE International Conference on Robotics and Automation (ICRA 2023