In contrast with the diversity of materials found in nature, most robots are designed with some combination of aluminum, stainless steel, and 3D-printed filament. Additionally, robotic systems are typically assumed to follow basic rigid-body dynamics. However, several examples in nature illustrate how changes in physical material properties yield functional advantages. In this paper, we explore how physical materials (non-rigid bodies) affect the functional performance of a hopping robot. In doing so, we address the practical question of how to model and simulate material properties. Through these simulations we demonstrate that material gradients in the leg of a single-limb hopper provide functional advantages compared to homogeneous designs. For example, when considering incline ramp hopping, a material gradient with increasing density provides a 35% reduction in tracking error and a 23% reduction in power consumption compared to homogeneous stainless steel. By providing bio-inspiration to the rigid limbs in a robotic system, we seek to show that future fabrication of robots should look to leverage the material anisotropies of moduli and density found in nature. This would allow for reduced vibrations in the system and would provide offsets of joint torques and vibrations while protecting their structural integrity against reduced fatigue and wear. This simulation system could inspire future intelligent material gradients of custom-fabricated robotic locomotive devices.

Successfully achieving bipedal locomotion remains challenging due to real-world factors such as model uncertainty, random disturbances, and imperfect state estimation. In this work, we propose a novel metric for locomotive robustness – the estimated size of the hybrid forward invariant set associated with the step-to-step dynamics. Here, the forward invariant set can be loosely interpreted as the region of attraction for the discrete-time dynamics. We illustrate the use of this metric towards synthesizing nominal walking gaits using a simulation-in-the-loop learning approach. Further, we leverage discrete-time barrier functions and a sampling-based approach to approximate sets that are maximally forward invariant. Lastly, we experimentally demonstrate that this approach results in successful locomotion for both flat-foot walking and multi-contact walking on the Atalante lower-body exoskeleton.

The ability to generate robust walking gaits on bipedal robots is key to their successful realization on hard-ware. To this end, this work extends the method of Hybrid Zero Dynamics (HZD) – which traditionally only accounts for locomotive stability via periodicity constraints under perfect impact events – through the inclusion of the saltation matrix with a view toward synthesizing robust walking gaits. By jointly minimizing the norm of the extended saltation matrix and the torque of the robot directly in the gait generation process, we demonstrate that the synthesized gaits are more robust than gaits generated with either term alone; these results are shown in simulation and on hardware for the AMBER-3M planar biped and the Atalante lower-body exoskeleton (both with and without a human subject). The end result is experimental validation that combining saltation matrices with HZD methods produces more robust bipedal walking in practice.

Experimental demonstration of complex robotic behaviors relies heavily on finding the correct controller gains. This painstaking process is often completed by a domain expert, requiring deep knowledge of the relationship between parameter values and the resulting behavior of the system. Even when such knowledge is possessed, it can take significant effort to navigate the nonintuitive landscape of possible parameter combinations. In this work, we explore the extent to which preference-based learning can be used to optimize controller gains online by repeatedly querying the user for their preferences. This general methodology is applied to two variants of control Lyapunov function based nonlinear controllers framed as quadratic programs, which provide theoretical guarantees but are challenging to realize in practice. These controllers are successfully demonstrated both on the planar underactuated biped, AMBER, and on the 3D underactuated biped, Cassie. We experimentally evaluate the performance of the learned controllers and show that the proposed method is repeatably able to learn gains that yield stable and robust locomotion.

Characterizing what types of exoskeleton gaits are comfortable for users, and understanding the science of walking more generally, require recovering a user’s utility landscape. Learning these landscapes is challenging, as walking trajectories are defined by numerous gait parameters, data collection from human trials is expensive, and user safety and comfort must be ensured. This work proposes the Region of Interest Active Learning (ROIAL) framework, which actively learns each user’s underlying utility function over a region of interest that ensures safety and comfort. ROIAL learns from ordinal and preference feedback, which are more reliable feedback mechanisms than absolute numerical scores. The algorithm’s performance is evaluated both in simulation and experimentally for three non-disabled subjects walking inside of a lower-body exoskeleton. ROIAL learns Bayesian posteriors that predict each exoskeleton user’s utility landscape across four exoskeleton gait parameters. The algorithm discovers both commonalities and discrepancies across users’ gait preferences and identifies the gait parameters that most influenced user feedback. These results demonstrate the feasibility of recovering gait utility landscapes from limited human trials.

This paper presents a framework that leverages both control theory and machine learning to obtain stable and robust bipedal locomotion without the need for manual parameter tuning. Traditionally, gaits are generated through trajectory optimization methods and then realized experimentally — a process that often requires extensive tuning due to differences between the models and hardware. In this work, the process of gait realization via hybrid zero dynamics (HZD) based optimization is formally combined with preference-based learning to systematically realize dynamically stable walking. Importantly, this learning approach does not require a carefully constructed reward function, but instead utilizes human pairwise preferences. The power of the proposed approach is demonstrated through two experiments on a planar biped AMBER-3M: the first with rigid point-feet, and the second with induced model uncertainty through the addition of springs where the added compliance was not accounted for in the gait generation or in the controller. In both experiments, the framework achieves stable, robust, efficient, and natural walking in fewer than 50 iterations with no reliance on a simulation environment. These results demonstrate a promising step in the unification of control theory and learning.

This paper presents a personalized gait optimization framework for lower-body exoskeletons. Rather than optimizing numerical objectives such as the mechanical cost of transport, our approach directly learns from user prefer-ences, e.g., for comfort. Building upon work in preference-based interactive learning, we present the CoSpar algorithm. CoSpar prompts the user to give pairwise preferences between trials and suggest improvements; as exoskeleton walking is a non-intuitive behavior, users can provide preferences more easily and reliably than numerical feedback. We show that CoSpar performs competitively in simulation and demonstrate a prototype implementation of CoSpar on a lower-body exoskeleton to optimize human walking trajectory features. In the experiments, CoSpar consistently found user-preferred parameters of the exoskeleton's walking gait, which suggests that it is a promising starting point for adapting and personalizing exoskeletons (or other assistive devices) to individual users.

Optimizing lower-body exoskeleton walking gaits for user comfort requires understanding users' preferences over a high-dimensional gait parameter space. However, existing preference-based learning methods have only explored low-dimensional domains due to computational limitations. To learn user preferences in high dimensions, this work presents LINECOSPAR, a human-in-the-loop preference-based framework that enables optimization over many parameters by iteratively exploring one-dimensional subspaces. Additionally, this work identifies gait attributes that characterize broader preferences across users. In simulations and human trials, we empirically verify that LINECOSPAR is a sample-efficient approach for high-dimensional preference optimization. Our analysis of the experimental data reveals a correspondence between human preferences and objective measures of dynamicity, while also highlighting differences in the utility functions underlying individual users' gait preferences. This result has implications for exoskeleton gait synthesis, an active field with applications to clinical use and patient rehabilitation.