Modeling and In-flight Torso Attitude Stabilization of a Jumping Quadruped

Abstract

This paper addresses the modeling and attitude control of jumping quadrupeds in low-gravity environments. First, a convex decomposition procedure is presented to generate high-accuracy and low-cost collision geometries for quadrupeds performing agile maneuvers. A hierarchical control architecture is then investigated, separating torso orientation tracking from the generation of suitable, collision-free, corresponding leg motions. Nonlinear Model Predictive Controllers (NMPCs) are utilized in both layers of the controller. To compute the necessary leg motions, a torque allocation strategy is employed that leverages the symmetries of the system to avoid self-collisions and simplify the respective NMPC. To plan periodic trajectories online, a Finite State Machine (FSM)-based weight switching strategy is also used. The proposed controller is first evaluated in simulation, where 90 degree rotations in roll, pitch, and yaw are stabilized in 6.3, 2.4, and 5.5 seconds, respectively. The performance of the controller is further experimentally demonstrated by stabilizing constant and changing orientation references. Overall, this work provides a framework for the development of advanced model-based attitude controllers for jumping legged systems.

Figures (11)

• Figure 1: Instances of Olympus changing its yaw orientation by moving its legs
• Figure 2: Olympus's leg with the corresponding frames
• Figure 3: Procedure for generating the collision geometry
• Figure 4: The curved arrows indicate the direction of the leg movements, while the arrow tips/tails denote the direction of the induced torque. Roll degree of freedom: If the legs move together in the same direction in the $\tau_{\mathrm{x}}$ plane a net roll torque is induced in the torso (roll mapping), whereas if they move in opposite directions in the $\tau_{\mathrm{x}}$ plane, the roll torques almost cancel out (no roll mapping). Pitch/Yaw degree of freedom: To produce pitch moments, the legs must move near the $\tau_{\mathrm{y}}$ plane in unison from rear to front or vice versa (pitch mapping). To produce yaw moments, the legs of one side move from rear to front and the ones from the other side from front to rear near the $\tau_{\mathrm{z}}$ plane (yaw mapping).
• Figure 5: Illustration of the resetting algorithm on an example trajectory. The controller tracks the current phase setpoint ($\boldsymbol{\varphi}_{\mathrm{ref,i}}$). When the current joint position $\boldsymbol{\varphi}(t)$ enters the phase's ‘‘bubble" as per (\ref{['MPC::eq::state_trans']}), the next phase becomes active