This book, written by two major figures in adaptive control, provides a wealth of material for researchers, practitioners, and students. While some researchers in adaptive control may note the absence of a particular topic, the book‘s scope represents a high-gain instrument. It can be used by designers of control systems to enhance their work through the information on many new theoretical developments, and can be used by mathematical control theory specialists to adapt their research to practical needs. The book is strongly recommended to anyone interested in adaptive control.

Adaptive Control

Technological advancements have led to the development of numerous wearable robotic devices for the physical assistance and restoration of human locomotion. While many challenges remain with respect to the mechanical design of such devices, it is at least equally challenging and important to develop strategies to control them in concert with the intentions of the user. This work reviews the state-of-the-art techniques for controlling portable active lower limb prosthetic and orthotic (P/O) devices in the context of locomotive activities of daily living (ADL), and considers how these can be interfaced with the user’s sensory-motor control system. This review underscores the practical challenges and opportunities associated with P/O control, which can be used to accelerate future developments in this field. Furthermore, this work provides a classification scheme for the comparison of the various control strategies. As a novel contribution, a general framework for the control of portable gait-assistance devices is proposed. This framework accounts for the physical and informatic interactions between the controller, the user, the environment, and the mechanical device itself. Such a treatment of P/Os – not as independent devices, but as actors within an ecosystem – is suggested to be necessary to structure the next generation of intelligent and multifunctional controllers. Each element of the proposed framework is discussed with respect to the role that it plays in the assistance of locomotion, along with how its states can be sensed as inputs to the controller. The reviewed controllers are shown to fit within different levels of a hierarchical scheme, which loosely resembles the structure and functionality of the nominal human central nervous system (CNS). Active and passive safety mechanisms are considered to be central aspects underlying all of P/O design and control, and are shown to be critical for regulatory approval of such devices for real-world use. The works discussed herein provide evidence that, while we are getting ever closer, significant challenges still exist for the development of controllers for portable powered P/O devices that can seamlessly integrate with the user’s neuromusculoskeletal system and are practical for use in locomotive ADL.

/pdf/control-strategies-for-active-lower-extremity-prosthetics-5ojhkwsifh.pdf

Control strategies for active lower extremity prosthetics and orthotics: a review

https://hal.archives-ouvertes.fr/hal-01676474/document

Models, feedback control, and open problems of 3D bipedal robotic walking

This paper presents a human-inspired control approach to bipedal robotic walking: utilizing human data and output functions that appear to be intrinsic to human walking in order to formally design controllers that provably result in stable robotic walking. Beginning with human walking data, outputs-or functions of the kinematics-are determined that result in a low-dimensional representation of human locomotion. These same outputs can be considered on a robot, and human-inspired control is used to drive the outputs of the robot to the outputs of the human. The main results of this paper are that, in the case of both under and full actuation, the parameters of this controller can be determined through a human-inspired optimization problem that provides the best fit of the human data while simultaneously provably guaranteeing stable robotic walking for which the initial condition can be computed in closed form. These formal results are demonstrated in simulation by considering two bipedal robots-an underactuated 2-D bipedal robot, AMBER, and fully actuated 3-D bipedal robot, NAO-for which stable robotic walking is automatically obtained using only human data. Moreover, in both cases, these simulated walking gaits are realized experimentally to obtain human-inspired bipedal walking on the actual robots.

/pdf/human-inspired-control-of-bipedal-walking-robots-29pq1qynca.pdf

Human-Inspired Control of Bipedal Walking Robots

This paper presents a methodology for the development of control barrier functions (CBFs) through a backstepping inspired approach. Given a set defined as the superlevel set of a function, h, the main result is a constructive means for generating control barrier functions that guarantee forward invariance of this set. In particular, if the function defining the set has relative degree n, an iterative methodology utilizing higher order derivatives of h provably results in a control barrier function that can be explicitly derived. To demonstrate these formal results, they are applied in the context of bipedal robotic walking. Physical constraints, e.g., joint limits, are represented by control barrier functions and unified with control objectives expressed through control Lyapunov functions (CLFs) via quadratic program (QP) based controllers. The end result is the generation of stable walking satisfying physical realizability constraints for a model of the bipedal robot AMBER2.

/pdf/control-barrier-function-based-quadratic-programs-with-2uzmgsdfho.pdf

Control barrier function based quadratic programs with application to bipedal robotic walking

This letter presents a new notion of input-to-state safe control barrier functions (ISSf-CBFs), which ensure safety of nonlinear dynamical systems under input disturbances. Similar to how safety conditions are specified in terms of forward invariance of a set, input-to-state safety (ISSf) conditions are specified in terms of forward invariance of a slightly larger set. In this context, invariance of the larger set implies that the states stay either inside or very close to the smaller safe set; and this closeness is bounded by the magnitude of the disturbances. The main contribution of the letter is the methodology used for obtaining a valid ISSf-CBF, given a control barrier function (CBF). The associated universal control law will also be provided. Towards the end, we will study unified quadratic programs (QPs) that combine control Lyapunov functions (CLFs) and ISSf-CBFs in order to obtain a single control law that ensures both safety and stability in systems with input disturbances.

Input-to-State Safety with Control Barrier Functions

This paper presents a methodology for achieving efficient multi-domain underactuated bipedal walking on compliant robots by formally emulating gaits produced by the Spring Loaded Inverted Pendulum (SLIP). With the goal of achieving locomotion that displays phases of double and single support, a hybrid system model is formulated that faithfully represents the full-order dynamics of a compliant walking robot. The SLIP model is used as a bases for constructing human-inspired controllers that yield a dimension reduction through the use of hybrid zero dynamics. This allows for the formulation of an optimization problem that produces hybrid zero dynamics that best represents a SLIP model walking gait, while simultaneously ensuring the proper reduction in dimensionality that can be utilized to produce stable periodic orbits, i.e., walking gaits. The end result is stable robotic walking in simulation and, when implemented on the compliant robot ATRIAS, experimentally realized dynamic multi-domain locomotion.

Dynamic multi-domain bipedal walking with atrias through SLIP based human-inspired control

This paper presents the meta-algorithmic approach used to realize multi-contact walking on the humanoid robot, DURUS. This systematic methodology begins by decomposing human walking into a sequence of distinct events (e.g. heel-strike, toe-strike, and toe push-off). These events are converted into an alternating sequence of domains and guards, resulting in a hybrid system model of the locomotion. Through the use of a direct collocation based optimization framework, a walking gait is generated for the hybrid system model emulating human-like multi-contact walking behaviors – additional constraints are iteratively added and shaped from experimental evaluation to reflect the machine’s practical limitations. The synthesized gait is analyzed directly on hardware wherein feedback regulators are introduced which stabilize the walking gait, e.g., modulating foot placement. The end result is an energyoptimized walking gait that is physically implementable on hardware. The novelty of this work lies in the creation of a systematic approach for developing dynamic walking gaits on 3D humanoid robots: from formulating the hybrid system model to gait optimization to experimental validation refined to produce multi-contact 3D walking in experiment.

/pdf/algorithmic-foundations-of-realizing-multi-contact-27hm7ygu59.pdf

Algorithmic Foundations of Realizing Multi-Contact Locomotion on the Humanoid Robot DURUS

Bipedal robotic running remains a challenging benchmark in the field of control and robotics because of its highly dynamic nature and necessarily underactuated hybrid dynamics. Previous results have achieved bipedal running experimentally with a combination of theoretical results and heuristic application thereof. In particular, formal analysis of the hybrid system stability is given based on a theoretical model, but due to the gap between theoretical concepts and experimental reality, extensive tuning is necessary to achieve experimental success. In this paper, we present a formal approach to bridge this gap, starting from theoretical gait generation to a provably stable control implementation, resulting in bipedal robotic running. We first use a large-scale optimization to generate an energy-efficient running gait, subject to hybrid zero dynamics conditions and feasibility constraints which incorporate practical limitations of the robot model based on physical conditions. The stability of the gait is formally guaranteed in the hybrid system model with an input to state stability (ISS) based control law. This implementation improves the stability under practical control limitations of the system. Finally, the methodology is experimentally realized on the planar spring-legged bipedal robot, DURUS-2D, resulting in sustainable running at 1.75m/s. The paper, therefore, presents a formal method that takes the first step toward bridging the gap between theory and experiment.

https://dl.acm.org/doi/pdf/10.1145/3049797.3049823

Shishir Kolathaya

Papers

Input-to-State Safety with Control Barrier Functions

Input-to-State Safety with Control Barrier Functions

Dynamic multi-domain bipedal walking with atrias through SLIP based human-inspired control

Algorithmic Foundations of Realizing Multi-Contact Locomotion on the Humanoid Robot DURUS

Bipedal Robotic Running with DURUS-2D: Bridging the Gap between Theory and Experiment