Quadratic Programming Optimization for Bio-Inspired Thruster-Assisted Bipedal Locomotion on Inclined Slopes

Our work aims to make significant strides in understanding unexplored locomotion control paradigms based on the integration of posture manipulation and thrust vectoring. These techniques are commonly seen in nature, such as Chukar birds using their wings to run on a nearly vertical wall. In this work, we show quadratic programming with contact constraints which is then given to the whole body controller to map on robot states to produce a thruster-assisted slope walking controller for our state-of-the-art Harpy platform. Harpy is a bipedal robot capable of legged-aerial locomotion using its legs and thrusters attached to its main frame. The optimization-based walking controller has been used for dynamic locomotion such as slope walking, but the addition of thrusters to perform inclined slope walking has not been extensively explored. In this work, we derive a thruster-assisted bipedal walking with the quadratic programming (QP) controller and implement it in simulation to study its performance.

Enabling steep slope walking on Husky using reduced order modeling and quadratic programming

Wing-assisted inclined running (WAIR) observed in some young birds, is an attractive maneuver that can be extended to legged aerial systems. This study proposes a control method using a modified Variable Length Inverted Pendulum (VLIP) by assuming a fixed zero moment point and thruster forces collocated at the center of mass of the pendulum. A QP MPC is used to find the optimal ground reaction forces and thruster forces to track a reference position and velocity trajectory. Simulation results of this VLIP model on a slope of 40 degrees is maintained and shows thruster forces that can be obtained through posture manipulation. The simulation also provides insight to how the combined efforts of the thrusters and the tractive forces from the legs make WAIR possible in thruster-assisted legged systems.

Optimization free control and ground force estimation with momentum observer for a multimodal legged aerial robot

Legged-aerial multimodal robots can make the most of both legged and aerial systems. In this paper, we propose a control framework that bypasses heavy onboard computers by using an optimization-free Explicit Reference Governor that incorporates external thruster forces from an attitude controller. Ground reaction forces are maintained within friction cone constraints using costly optimization solvers, but the ERG framework filters applied velocity references that ensure no slippage at the foot end. We also propose a Conjugate momentum observer, that is widely used in Disturbance Observation to estimate ground reaction forces and compare its efficacy against a constrained model in estimating ground reaction forces in a reduced-order simulation of Husky.

Capture Point Control in Thruster-Assisted Bipedal Locomotion

Despite major advancements in control design that are robust to unplanned disturbances, bipedal robots are still susceptible to falling over and struggle to negotiate rough terrains. By utilizing thrusters in our bipedal robot, we can perform additional posture manipulation and expand the modes of locomotion to enhance the robot's stability and ability to negotiate rough and difficult-to-navigate terrains. In this paper, we present our efforts in designing a controller based on capture point control for our thruster-assisted walking model named Harpy and explore its control design possibilities. While capture point control based on centroidal models for bipedal systems has been extensively studied, the incorporation of external forces that can influence the dynamics of linear inverted pendulum models, often used in capture point-based works, has not been explored before. The inclusion of these external forces can lead to interesting interpretations of locomotion, such as virtual buoyancy studied in aquatic-legged locomotion. This paper outlines the dynamical model of our robot, the capture point method we use to assist the upper body stabilization, and the simulation work done to show the controller's feasibility.

Thruster-Assisted Incline Walking

In this study, our aim is to evaluate the effectiveness of thruster-assisted steep slope walking for the Husky Carbon, a quadrupedal robot equipped with custom-designed actuators and plural electric ducted fans, through simulation prior to conducting experimental trials. Thruster-assisted steep slope walking draws inspiration from wing-assisted incline running (WAIR) observed in birds, and intriguingly incorporates posture manipulation and thrust vectoring, a locomotion technique not previously explored in the animal kingdom. Our approach involves developing a reduced-order model of the Husky robot, followed by the application of an optimization-based controller utilizing collocation methods and dynamics interpolation to determine control actions. Through simulation testing, we demonstrate the feasibility of hardware implementation of our controller.

Narrow-Path, Dynamic Walking Using Integrated Posture Manipulation and Thrust Vectoring

This research concentrates on enhancing the navigational capabilities of Northeastern Universitys Husky, a multi-modal quadrupedal robot, that can integrate posture manipulation and thrust vectoring, to traverse through narrow pathways such as walking over pipes and slacklining. The Husky is outfitted with thrusters designed to stabilize its body during dynamic walking over these narrow paths. The project involves modeling the robot using the HROM (Husky Reduced Order Model) and developing an optimal control framework. This framework is based on polynomial approximation of the HROM and a collocation approach to derive optimal thruster commands necessary for achieving dynamic walking on narrow paths. The effectiveness of the modeling and control design approach is validated through simulations conducted using Matlab.

Towards dynamic Narrow path walking on NU's Husky

This research focuses on enabling Northeastern University's Husky, a multi-modal quadrupedal robot, to navigate narrow paths akin to various animals in nature. The Husky is equipped with thrusters to stabilize its body during dynamic maneuvers, addressing challenges inherent in aerial-legged systems. The approach involves modeling the robot as HROM (Husky Reduced Model) and creating an optimal control framework using linearized dynamics for narrow path walking. The thesis introduces a gait scheduling method to generate an open-loop walking gait and validates these gaits through a high-fidelity Simscape simulation. Experimental results of the open-loop walking are presented, accompanied by potential directions for advancing this robotic system.

A Letter on Progress Made on Husky Carbon: A Legged-Aerial, Multi-modal Platform

Animals, such as birds, widely use multi-modal locomotion by combining legged and aerial mobility with dominant inertial effects. The robotic biomimicry of this multi-modal locomotion feat can yield ultra-flexible systems in terms of their ability to negotiate their task spaces. The main objective of this paper is to discuss the challenges in achieving multi-modal locomotion, and to report our progress in developing our quadrupedal robot capable of multi-modal locomotion (legged and aerial locomotion), the Husky Carbon. We report the mechanical and electrical components utilized in our robot, in addition to the simulation and experimentation done to achieve our goal in developing a versatile multi-modal robotic platform.