Stochastic analysis and adaptive control studies in legged systems

Er, Güner Dilşad
Underactuated legged robots depict highly nonlinear and complex dynamical behaviors that create significant challenges in accurately modeling system dynamics using both first principles and system identification approaches. Hence, the design of stabilizing controllers becomes more challenging due to inaccurate modeling. Suppose physical parameters on mathematical models have miscalibrations due to uncertainty in identifying and modeling processes. In that case, designed controllers could perform poorly or even result in unstable responses. Moreover, these parameters can change over time due to operation and environmental conditions. In that respect, analogous to a living organism modifying its behavior in response to novel conditions, adapting/updating system parameters, such as spring constant to compensate for modeling errors, could provide the advantage of constructing a stable gait level controller without needing “exact” dynamical parameter values. The first part of this thesis presents an online, model-based adaptive control approach for an underactuated planar hexapod robot’s pronking behavior adopted from antelope species. Systematic simulation studies show that the adaptive control policy is robust to high levels of parameter uncertainties compared to a non-adaptive model-based dead-beat controller. In the second part of the study, an efficient estimation method based on unscented transformation is proposed to quantify the stochastic stability characteristics of metastable legged systems. Unlike previous methods requiring high-dimensional state space discretization for a broad set of initial conditions to estimate the stability characteristics, this study aims to assess controller performances and analyze parametric dependencies with fewer experiments. In the proposed approach, the unscented transformation is employed because it utilizes prior knowledge of the noise statistics, and provides informed choices of initial conditions for the experiments, thus, reducing the computational complexity significantly. Additionally, it allows dealing with multiple sources of uncertainties and high-dimensional system dynamics. Finally, the capability of the proposed method is shown via analyzing a one-dimensional hopper and an underactuated bipedal walking simulation with a hybrid zero dynamics controller.


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Citation Formats
G. D. Er, “Stochastic analysis and adaptive control studies in legged systems,” M.S. - Master of Science, Middle East Technical University, 2022.