Developing Walking Controllers for a Bipedal Robot Using Analytical Models and Data Driven Approaches

The control of bipedal robots poses significant challenges due to their intricate dynamics and limited actuation, often rendering them only partially controllable. Traditional control methods employ full-order models to plan joint movements and achieve desired robot motion. However, this approach involves complex numerical integration of the model, consuming considerable computational resources and impeding real-time control. Alternatively, simplified models can capture essential aspects of a robot's dynamics and offer faster solutions for real-time control. While this method has effectively controlled lightweight, upper-body-free robots resembling point-mass inverted pendulums, it becomes more complex for robots like biped Digit with heavier torsos. This research project focuses on data-driven linear and nonlinear modeling to better represent the robot's dynamics than conventional models, such as the Linear Inverted Pendulum model. The developed model supports the creation of a model-based stepping controller, stabilized through appropriate feedback control parameters, enabling stable steady-state walking and velocity tracking. Furthermore, it leverages the analytical models and data-extracted feasible action regions to formulate quadratic optimization problems. These problems find applications in safe and optimal control, particularly in scenarios where precise foot placement, such as navigating environments with obstacles, is essential. This project introduces the non-homogeneous linear inverted pendulum model (NH-LIPM), enhancing the conventional LIPM by incorporating a non-homogeneous function into the equation. This addresses dynamics that deviate from the LIPM due to simplifications like assumptions about the center of mass location. The study takes a step further by introducing a forcing function to the model, accommodating biped dynamics influenced by external forces, such as toe/ankle torques or damping. The forced-NH-LIPM (F-NH-LIPM) is introduced for walking control, capable of modeling known and controllable external forces such as toe/ankle torque and damping. This knowledge enables utilizing footstep and ankle torque as control inputs. The proposed analytical models facilitate asymmetric stepping, allowing the robot to perform non-standard steps, critical for navigating constrained environments and obstacles. Model-predictive control (MPC) based on the analytical model enables the selection of control states within a discrete time horizon to guide the robot to its desired state. Finally, the project explores adaptive techniques to stabilize the robot when its dynamics deviate from the model, enhancing the adaptability and robustness of bipedal robots.