Data-Driven Predictive Control for Robust Exoskeleton Locomotion

Exoskeleton locomotion must be robust while being adaptive to different users with and without payloads. To address these challenges, this work introduces a data-driven predictive control (DDPC) framework to synthesize walking gaits for lower-body exoskeletons, employing Hankel matrices and a state transition matrix for its data-driven model. The proposed approach leverages DDPC through a multi-layer architecture. At the top layer, DDPC serves as a planner employing Hankel matrices and a state transition matrix to generate a data-driven model that can learn and adapt to varying users and payloads. At the lower layer, our method incorporates inverse kinematics and passivity-based control to map the planned trajectory from DDPC into the full-order states of the lower-body exoskeleton. We validate the effectiveness of this approach through numerical simulations and hardware experiments conducted on the Atalante lower-body exoskeleton with different payloads. Moreover, we conducted a comparative analysis against the model predictive control (MPC) framework based on the reduced-order linear inverted pendulum (LIP) model. Through this comparison, the paper demonstrates that DDPC enables robust bipedal walking at various velocities while accounting for model uncertainties and unknown perturbations.

Explosive Legged Robotic Hopping: Energy Accumulation and Power Amplification via Pneumatic Augmentation

We present a novel pneumatic augmentation to traditional electric motor-actuated legged robot to increase intermittent power density to perform infrequent explosive hopping behaviors. The pneumatic system is composed of a pneumatic pump, a tank, and a pneumatic actuator. The tank is charged up by the pump during regular hopping motion that is created by the electric motors. At any time after reaching a desired air pressure in the tank, a solenoid valve is utilized to rapidly release the air pressure to the pneumatic actuator (piston) which is used in conjunction with the electric motors to perform explosive hopping, increasing maximum hopping height for one or subsequent cycles. We show that, on a custom-designed one-legged hopping robot, without any additional power source and with this novel pneumatic augmentation system, their associated system identification and optimal control, the robot is able to realize highly explosive hopping with power amplification per cycle by a factor of approximately 5.4 times the power of electric motor actuation alone.

Terrestrial Locomotion of PogoX: From Hardware Design to Energy Shaping and Step-to-step Dynamics Based Control

We present a novel controller design on a robotic locomotor that combines an aerial vehicle with a spring-loaded leg. The main motivation is to enable the terrestrial locomotion capability on aerial vehicles so that they can carry heavy loads: heavy enough that flying is no longer possible, e.g., when the thrust-to-weight ratio (TWR) is small. The robot is designed with a pogo-stick leg and a quadrotor, and thus it is named as PogoX. We show that with a simple and lightweight spring-loaded leg, the robot is capable of hopping with TWR $<1$. The control of hopping is realized via two components: a vertical height control via control Lyapunov function-based energy shaping, and a step-to-step (S2S) dynamics based horizontal velocity control that is inspired by the hopping of the Spring-Loaded Inverted Pendulum (SLIP). The controller is successfully realized on the physical robot, showing dynamic terrestrial locomotion of PogoX which can hop at variable heights and different horizontal velocities with robustness to ground height variations and external pushes.

Data-driven Step-to-step Dynamics based Adaptive Control for Robust and Versatile Underactuated Bipedal Robotic Walking

This paper presents a framework for synthesizing bipedal robotic walking that adapts to unknown environment and dynamics error via a data-driven step-to-step (S2S) dynamics model. We begin by synthesizing an S2S controller that stabilizes the walking using foot placement through nominal S2S dynamics from the hybrid linear inverted pendulum (H-LIP) model. Next, a data-driven representation of the S2S dynamics of the robot is learned online via classical adaptive control methods. The desired discrete foot placement on the robot is thereby realized by proper continuous output synthesis capturing the data-driven S2S controller coupled with a low-level tracking controller. The proposed approach is implemented in simulation on an underactuated 3D bipedal robot, Cassie, and improved reference velocity tracking is demonstrated. The proposed approach is also able to realize walking behavior that is robustly adaptive to unknown loads, inaccurate robot models, external disturbance forces, biased velocity estimation, and unknown slopes.

From Human Walking to Bipedal Robot Locomotion: Reflex Inspired Compensation on Planned and Unplanned Downsteps

Humans are able to negotiate downstep behaviors -- both planned and unplanned -- with remarkable agility and ease. The goal of this paper is to systematically study the translation of this human behavior to bipedal walking robots, even if the morphology is inherently different. Concretely, we begin with human data wherein planned and unplanned downsteps are taken. We analyze this data from the perspective of reduced-order modeling of the human, encoding the center of mass (CoM) kinematics and contact forces, which allows for the translation of these behaviors into the corresponding reduced-order model of a bipedal robot. We embed the resulting behaviors into the full-order dynamics of a bipedal robot via nonlinear optimization-based controllers. The end result is the demonstration of planned and unplanned downsteps in simulation on an underactuated walking robot.

Robust Disturbance Rejection for Robotic Bipedal Walking: System-Level-Synthesis with Step-to-step Dynamics Approximation

We present a stepping stabilization control that addresses external push disturbances on bipedal walking robots. The stepping control is synthesized based on the step-to-step (S2S) dynamics of the robot that is controlled to have an approximately constant center of mass (COM) height. We first learn a linear S2S dynamics with bounded model discrepancy from the undisturbed walking behaviors of the robot, where the walking step size is taken as the control input to the S2S dynamics. External pushes are then considered as disturbances to the learned S2S (L-S2S) dynamics. We then apply the system-level-synthesis (SLS) approach on the disturbed L-S2S dynamics to robustly stabilize the robot to the desired walking while satisfying the kinematic constraints of the robot. We successfully realize the proposed approach on the walking of the bipedal robot AMBER and Cassie subject to push disturbances, showing that the approach is general, effective, and computationally-efficient for robust disturbance rejection.

Bipedal Walking on Constrained Footholds: Momentum Regulation via Vertical COM Control

This paper presents an online walking gait synthesis and a feedback control methodology to enable stable walking on constrained footholds for bipedal robots. For this challenging task, the foot placement and center of pressure cannot be changed, which hinders the application of state-of-art stepping controllers or zero-moment-point (ZMP) based approaches for walking generation. As a result, this paper takes a different approach to modulate the change of the angular momentum about the foot-ground contact pivot at the discrete impact with vertical center of mass (COM) velocity. We utilize the underactuated Linear Inverted Pendulum (LIP) model for approximating the underactuated walking dynamics to provide the desired post-impact angular momentum for each step. Outputs are constructed via online optimization combined with closed-form polynomials and then tracked via a quadratic program based controller. This method is implemented online on two robot models, AMBER and Cassie, for which stable walking behaviors with constrained footholds are realized on flat ground, stairs, and randomly located stepping stones.

SLIP Walking over Rough Terrain via H-LIP Stepping and Backstepping-Barrier Function Inspired Quadratic Program

We present an advanced and novel control method to enable actuated Spring Loaded Inverted Pendulum model to walk over rough and challenging terrains. The high-level philosophy is the decoupling of the controls of the vertical and horizontal states. The vertical state is controlled via Backstepping-Barrier Function (BBF) based quadratic programs: a combination of control Lyapunov backstepping and control barrier function, both of which provide inequality constraints on the inputs. The horizontal state is stabilized via Hybrid-Linear Inverted Pendulum (H-LIP) based stepping, which has a closed-form formulation. Therefore, the implementation is computationally-efficient. We evaluate our method in simulation, which demonstrates the aSLIP walking over various terrains, including slopes, stairs, and general rough terrains with uncertainties.

3D Underactuated Bipedal Walking via H-LIP based Gait Synthesis and Stepping Stabilization

In this paper, we present a Hybrid-Linear Inverted Pendulum (H-LIP) based approach for synthesizing and stabilizing 3D underactuated bipedal walking. The H-LIP model is proposed to capture the essential components of the underactuated part and actuated part of the robotic walking. The walking gait of the robot is then synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive their stepping stabilization. The step-to-step (S2S) dynamics of the H-LIP is then utilized to approximate the S2S dynamics of the horizontal state of the center of mass (COM) of the robotic walking, which results in a H-LIP based stepping controller to provide desired step sizes to stabilize the robotic walking. By realizing the desired step sizes, the robot achieves dynamic and stable walking. The approach is evaluated in both simulation and experiment on the 3D underactuated bipedal robot Cassie, which demonstrate dynamic walking behaviors with both versatility and robustness.