Enhancing Quadruped Locomotion Stability with Reaction Wheel Systems and Model Predictive Control

Abstract

The development of quadruped robots offers a mobility solution that allows robot agents to navigate complicated terrains, making them extremely versatile robots in a variety of environments. Today, there are a number of research challenges facing quadruped development. First, the current state-of-the-art quadruped suffers from under-actuation during the majority of its use cases such as trotting and running. Second, the non-linear contact dynamics of legged systems make them complicated control systems to model.

In the first part of this thesis, we address the issue of under-actuation by introducing a prototype reaction wheel system that gives quadruped robots enhanced attitude stabilization ability. The dynamics of reaction wheel actuation systems allow for a straightforward linearization of the robot dynamics in comparison to other inertial stabilization appendages such as tails. We model the system as a single gyrostat and simplify the dynamics to pose the problem as a linear discrete-time trajectory optimization problem that can be solved as a quadratic program. The linear MPC is implemented on hardware at 1000hz while reasoning about the speed and torque limits of the reaction wheel systems.

The second part of the thesis explores implementing a novel Contact Implicit Model Predictive Control (CI-MPC) system on hardware. We introduce a control stack that does not rely on explicit contact mode specification, and we demonstrated that the CI-MPC is capable of solving Linear Complementary Problem (LCP) contact dynamics on hardware in real-time.

The final part of the thesis proposes a method that can reliably identify inertial parameters for quadruped systems that be used for model-based control algorithms such as the two mentioned above. We introduce a two-step calibration routine to identify the planar center of mass (CoM) position and the effective centroidal dynamics parameters of any quadruped using only joint sensors and an inertial measurement unit (IMU). Our proposed calibration routine consists of two steps: A bisection search method is used to locate the position of the planar CoM, and a sinusoidal excitation method is used to extract moments of inertia about each body axis. We verify the inertial parameter identification method in simulation, and we implemented the center of mass finding algorithm in both simulation and hardware. The results of hardware CoM finding experiments verified in a balancing controller that requires 5mm CoM position accuracy.