Safe navigation in real-time is an essential task for humanoid robots in real-world deployment. Since humanoid robots are inherently underactuated thanks to unilateral ground contacts, a path is considered safe if it is obstacle-free and respects the robot's physical limitations and underlying dynamics. Existing approaches often decouple path planning from gait control due to the significant computational challenge caused by the full-order robot dynamics. In this work, we develop a unified, safe path and gait planning framework that can be evaluated online in real-time, allowing the robot to navigate clustered environments while sustaining stable locomotion. Our approach uses the popular Linear Inverted Pendulum (LIP) model as a template model to represent walking dynamics. It incorporates heading angles in the model to evaluate kinematic constraints essential for physically feasible gaits properly. In addition, we leverage discrete control barrier functions (DCBF) for obstacle avoidance, ensuring that the subsequent foot placement provides a safe navigation path within clustered environments. To guarantee real-time computation, we use a novel approximation of the DCBF to produce linear DCBF (LDCBF) constraints. We validate the proposed approach in simulation using a Digit robot in randomly generated environments. The results demonstrate that our approach can generate safe gaits for a nontrivial humanoid robot to navigate environments with randomly generated obstacles in real-time.

Traditional one-step preview planning algorithms for bipedal locomotion struggle to generate viable gaits when walking across terrains with restricted footholds, such as stepping stones. To overcome such limitations, this paper introduces a novel multi-step preview foot placement planning algorithm based on the step-to-step discrete evolution of the Divergent Component of Motion (DCM) of walking robots. Our proposed approach adaptively changes the step duration and the swing foot trajectory for optimal foot placement under constraints, thereby enhancing the long-term stability of the robot and significantly improving its ability to navigate environments with tight constraints on viable footholds. We demonstrate its effectiveness through various simulation scenarios with complex stepping-stone configurations and external perturbations. These tests underscore its improved performance for navigating foothold-restricted terrains, even with external disturbances.

Locomotion on dynamic rigid surface (i.e., rigid surface accelerating in an inertial frame) presents complex challenges for controller design, which are essential to address for deploying humanoid robots in dynamic real-world environments such as moving trains, ships, and airplanes. This paper introduces a real-time, provably stabilizing control approach for humanoid walking on periodically swaying rigid surface. The first key contribution is an analytical extension of the classical angular momentum-based linear inverted pendulum model from static to swaying grounds whose motion period may be different than the robot's gait period. This extension results in a time-varying, nonhomogeneous robot model, which is fundamentally different from the existing pendulum models. We synthesize a discrete footstep control law for the model and derive a new set of sufficient stability conditions that verify the controller's stabilizing effect. Finally, experiments conducted on a Digit humanoid robot, both in simulations and on hardware, demonstrate the framework's effectiveness in addressing bipedal locomotion on swaying ground, even under uncertain surface motions and unknown external pushes.

We present a framework to generate periodic trajectory references for a 3D under-actuated bipedal robot, using a linear inverted pendulum (LIP) based controller with adaptive neural regulation. We use the LIP template model to estimate the robot's center of mass (CoM) position and velocity at the end of the current step, and formulate a discrete controller that determines the next footstep location to achieve a desired walking profile. This controller is equipped on the frontal plane with a Neural-Network-based adaptive term that reduces the model mismatch between the template and physical robot that particularly affects the lateral motion. Then, the foot placement location computed for the LIP model is used to generate task space trajectories (CoM and swing foot trajectories) for the actual robot to realize stable walking. We use a fast, real-time QP-based inverse kinematics algorithm that produces joint references from the task space trajectories, which makes the formulation independent of the knowledge of the robot dynamics. Finally, we implemented and evaluated the proposed approach in simulation and hardware experiments with a Digit robot obtaining stable periodic locomotion for both cases.

For amputees, walking on sloped surfaces is one of the most challenging tasks in their daily lives. Unfortunately, designing a prosthesis that can effectively adapt to varying terrain is an ongoing problem. In this paper, we propose a unified control scheme that enables a powered transfemoral prosthesis to perform human-like walking on sloped terrains regardless of the slope and without any knowledge of the upcoming slope. The control scheme implements impedance control and trajectory tracking during the stance and swing phase, respectively. In the impedance control scheme, properly tuned impedance parameters are used to provide a stable and compliant stance phase that adapts to the slope of the ground. During the swing phase, the system is controlled by a Proportional-Derivative (PD) controller to track the desired trajectories based on cubic Bezier polynomials. These trajectories were obtained by solving an offline optimization problem compared to human slope walking data. Any slope walking trajectories can be generated online by using the optimized Bezier coefficients. At the terminal swing phase, a low gain PD controller is utilized to adapt to the unexpected terrains and smoothly track the generated trajectories. The proposed control framework is implemented on a powered transfemoral prosthesis, AMPRO II, on various slopes. The results validate the controller's ability to adapt to terrain inclinations within the range of ± 10°.

Powered transfemoral prostheses are robotic systems that aim to restore the mobility of transfemoral amputees by mimicking the functionalities of healthy human legs. The advantage of using a powered prosthetic device is the enhanced performance on various terrains. One of the most frequent terrain found during daily locomotion (other than flat ground) is the surface with slope. In this work, we introduce a framework to generate upslope walking gaits automatically utilizing an online algorithmic formulation. This approach is inspired from analyzing human gait characteristics during upslope walking. In particularly, it is found that the ankle and knee trajectories of upslope walking share a similar pattern with flat ground walking during the middle section (from 20% to 80%) of one step. This observation motivates us to propose an approach of blending the first portion of nominal flat ground gaits with a set of cubic splines to achieve upslope gaits. Importantly, parameters of these cubic splines are solved using an online optimization, which gives the users ability to traverse in different terrains without using any intention detection algorithm. For the last portion of a step, an impedance controller with low gains is considered upon the contact of prosthetic legs to the ground, which allows the users to step onto unknown terrains. The proposed framework is validated on a custom transfemoral prosthesis AMPRO II with showing automatic motion switches between flat ground and upslope walking.

Lower-limb prostheses provide a prime example of cyber-physical systems (CPSs) requiring the synergistic development of sensing, algorithms, and controllers. With a view towards better understanding CPSs of this form, this paper presents a systematic methodology using multidomain hybrid system models and optimization-based controllers to achieve human-like multicontact prosthetic walking on a custom-built prosthesis: AMPRO. To achieve this goal, unimpaired human locomotion data is collected and the nominal multicontact human gait is studied. Inspired by previous work which realized multicontact locomotion on the bipedal robot AMBER2, a hybrid system-based optimization problem utilizing the collected reference human gait as reference is utilized to formally design stable multicontact prosthetic gaits that can be implemented on the prosthesis directly. Leveraging control methods that stabilize bipedal walking robots–control Lyapunov function-based quadratic programs coupled with variable impedance control–an online optimization-based controller is formulated to realize the designed gait in both simulation and experimentally on AMPRO. Improved tracking and energy efficiency are seen when this methodology is implemented experimentally. Importantly, the resulting multicontact prosthetic walking captures the essentials of natural human walking both kinematically and kinetically.

This demonstration presents an unimpaired subject walking with a custom built self-contained powered transfemoral prosthesis: AMPRO, which is controlled by a novel nonlinear real-time optimization based controller. To achieve the behaviors that will be demonstrated, controllers that have been successfully implemented on bipedal walking robots are translated to the prosthesis with the goal of achieving natural human-like walking while minimizing power consumption. To achieve this goal, we begin by collecting reference human locomotion data via Inertial measurement Units (IMUs). This data forms the basis for an optimization problem that generates virtual constraints for the prosthesis that provably yields walking in simulation. Utilizing methods that have proven successful in generating stable robotic locomotion, control Lyapunov function (CLF) based Quadratic Programs (QPs) are utilized to optimally track the resulting desired trajectories. The parameterization of the trajectories is determined through a combination of on-board sensing on the prosthesis together with IMU data, thereby coupling the actions of the user with the controller. Finally, impedance control is integrated into the QP yielding an optimization based control law that displays remarkable tracking and robustness, outperforming traditional PD and impedance control strategies.