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

1. National Technical University of Athens, Greece
2. Norwegian University of Science and Technology, Norway

To be presented at the International Symposium of Robotics Research (ISRR) 2024

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.

Collision Modeling & Control Architecture

Control architecture overview: The proposed controller has a hierarchical structure. The Body Planner calculates the torso’s trajectory to track a reference orientation, while the Leg Planner determines the leg motions necessary to execute the reorientation maneuver.

Body Planner: The Body Planner considers the torso as a rigid body with fixed inertia. It calculates the torso’s trajectory to track a reference orientation by considering the legs as torque-producing actuators.

Leg Planner: The Leg Planner uses a nonlinear MPC to generate the motion required to track the torque computed by the Body Planer for one leg.

Resetting Strategy: When the leg reaches the boundary of the workspace, moving to a resetting point—where it can efficiently resume tracking the reference torque— conflicts with the short-term objectives of the MPC. In order to plan periodic trajectories online, the Leg Planner MPC is wrapped by a Finite State Machine that provides specific state references and penalty weights.

Allocation Module: By leveraging the system symmetries, the torque tracking problem is solved for one leg (the primary leg), and then the optimal joint trajectories of that leg are mapped in the others, avoiding self-collisions in the process.

Allocation Module: The allocation couples the movement of the legs, and thus the controller operates in distinct modes for Roll, Pitch and Yaw.

Collision Modelling: The link geometries are decomposed into a union of smaller convex shapes, offering a good compromise between simplification and fidelity. This approach reduces collision checking and enables real-time simulation without restricting the range of motion of the legs.

Results

Simulation results from tracking 90 degree turns in roll, pitch and yaw.

Mass ablation study results. The influence of increasing the paw or torso mass is investigated. The controller managed to stabilize the orientation in all cases, showcasing its robustness.

Roll experimental results.

Yaw experimental results.

Experiments

In the first set of experiments, the controller is tasked to track 90 degree rotations in roll and yaw.

In this set of experiments, the controller is tasked to track changing orientation references. In the final maneuver, it continues to turn in the positive direction to minimize the distance metric. The plot references for these maneuvers are shifted (+360 degrees) to showcase the controller convergence.

BibTeX

@article{papadakis2024olympusmpc, title={Modeling and In-flight Torso Attitude Stabilization of a Jumping Quadruped}, author={Papadakis, Michail and Olsen, Jørgen Anker and Poulakakis, Ioannis and Alexis, Kostas}, journal={arXiv preprint arXiv:2409.14567}, year={2024}, url={https://arxiv.org/abs/2409.14567} }