Team Members: Aditya Bondada, Harin Kumar Nallaguntla
In this project, we focused on modeling a planar robot as a three-link biped, assuming only one foot is in contact with the ground at any given time. We derived the equations of motion using Lagrangian formalism and computed the state space representation and zero dynamics equations. Our goal was to design optimization-based gaits and develop a non-linear feedback controller to maintain stability.
The three-link biped consists of two legs and a torso, modeled as a planar mechanism. We defined the generalized coordinates and velocities for the biped and computed the positions and velocities of various points using forward kinematics and homogeneous transformations.
We derived the equations of motion using the Lagrangian method, considering kinetic and potential energies. The equations were formulated as a set of coupled non-linear differential equations. We extended the model to include the double support phase, where both feet touch the ground.
We simulated the zero dynamics of the three-link biped in the sagittal plane using Bezier interpolation for gait design. We used optimization to find the optimal initial conditions for the zero dynamics states and the Bezier coefficients, ensuring smooth and efficient walking gaits.
We implemented a control strategy using feedback linearization. This involved computing the control action required to track desired joint angles by canceling out nonlinearities in the system. We combined this with a PD controller to maintain balance and ensure smooth gait transitions.
Our simulations demonstrated successful gait generation and stability maintenance. The feedback linearization technique, combined with the PD controller, provided effective control for the bipedal robot. The model accurately simulated walking gaits, including leg switch events during the double-support phase.
This project enhanced our understanding of legged robotics and bipedal locomotion. We successfully modeled and controlled a three-link biped, designing energetically efficient gaits and implementing a robust control strategy.