Kinematic Chain Monoids for Real-Time Kinodynamic Trajectory Optimization in Legged Robots

Dynamics Factor Graph (DFG) is a graphical framework to solve dynamics problems and kinodynamic motion planning problems with full consideration of whole-body dynam- ics and contacts. In this thesis I will present DFG and explain the different variables and constraints being used in legged robot trajectory optimization using DFG. In chapter 2 I will explain DFG’s and the challenges working with them as a whole body motion plan- ning framework. In chapter 3 I will present a novel formulation of kinematic chains as monoids, which provides a concise representation of the kinodynamics of the limbs of a walking robot. The proposed approach enables easier and more efficient constraints in trajectory planning optimization for robots assuming massless legs. I will introduce the constraints required to integrate kinematic chains in a factor-graph and demonstrate the applicability of these constraints in the Unitree A1 quadruped. In chapter 4 I will present simulation results done with chain dynamic factor graphs and compare with dynamic factor graphs and other related work done in the field.
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