Organizational Unit:

Institute for Robotics and Intelligent Machines (IRIM)

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https://hdl.handle.net/1853/70657

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Organizational Unit

Biorobotics and Human Modeling Lab

Organizational Unit

Humanoid Robotics Laboratory

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Publication Search Results

Now showing 1 - 10 of 17

Time Dependent Control Lyapunov Functions and Hybrid Zero Dynamics for Stable Robotic Locomotion

(Georgia Institute of Technology, 2016-07) Kolathaya, Shishir ; Hereid, Ayonga ; Ames, Aaron D.

Implementing state-based parameterized periodic trajectories on complex robotic systems, e.g., humanoid robots, can lead to instability due to sensor noise exacerbated by dynamic movements. As a means of understanding this phenomenon, and motivated by field testing on the humanoid robot DURUS, this paper presents sufficient conditions for the boundedness of hybrid periodic orbits (i.e., boundedness of walking gaits) for time dependent control Lyapunov functions. In particular, this paper considers virtual constraints that yield hybrid zero dynamics with desired outputs that are a function of time or a state-based phase variable. If the difference between the phase variable and time is bounded, we establish exponential boundedness to the zero dynamics surface. These results are extended to hybrid dynamical systems, establishing exponential boundedness of hybrid periodic orbits, i.e., we show that stable walking can be achieved through time-based implementations of state-based virtual constraints. These results are verified on the bipedal humanoid robot DURUS both in simulation and experimentally; it is demonstrated that a close match between time based tracking and state based tracking can be achieved as long as there is a close match between the time and phase based desired output trajectories.
Unification of Locomotion Pattern Generation and Control Lyapunov Function-Based Quadratic Programs

(Georgia Institute of Technology, 2016-07) Chao, Kenneth Y. ; Powell, Matthew J. ; Ames, Aaron D. ; Hur, Pilwon

This paper presents a novel method of combining real-time walking pattern generation and constrained nonlinear control to achieve robotic walking under Zero-Moment Point (ZMP) and torque constraints. The proposed method leverages the fact that existing solutions to both walking pattern generation and constrained nonlinear control have been independently constructed as Quadratic Programs (QPs) and that these constructions can be related through an equality constraint on the instantaneous acceleration of the center of mass. Speci cally, the proposed method solves a single Quadratic Program which incorporates elements from Model Predictive Control (MPC) based center of mass planning methods and from rapidly exponentially stabilizing control Lyapunov function (RES-CLF) methods. The resulting QP-based controller simultaneously solves for a COM trajectory that satis es ZMP constraints over a future horizon while also producing joint torques consistent with instantaneous acceleration, torque, ZMP and RES-CLF constraints. The method is developed for simulation and experimental study on a seven-link, planar robot.
Correct-By-Construction Adaptive Cruise Control: Two Approaches

(Georgia Institute of Technology, 2016-07) Nilsson, Petter ; Hussien, Omar ; Balkan, Ayca ; Chen, Yuxiao ; Ames, Aaron A. D. ; Grizzle, Jessy ; Ozay, Necmiye ; Peng, Huei ; Tabuada, Paulo

Motivated by the challenge of developing control software provably meeting specifications for real world problems, this paper applies formal methods to adaptive cruise control (ACC). Starting from a Linear Temporal Logic specification for ACC, obtained by interpreting relevant ACC standards, we discuss in this paper two different control software synthesis methods. Each method produces a controller that is correct-by-construction, meaning that trajectories of the closed-loop systems provably meet the specification. Both methods rely on fixed-point computations of certain set-valued mappings. However, one of the methods performs these computations on the continuous state space whereas the other method operates on a finite-state abstraction. While controller synthesis is based on a low-dimensional model, each controller is tested on CarSim, an industry-standard vehicle simulator. Our results demonstrate several advantages over classical control design techniques. First, a formal approach to control design removes potential ambiguity in textual specifications by translating them into precise mathematical requirements. Second, because the resulting closed-loop system is known a priori to satisfy the specification, testing can then focus on the validity of the models used in control design and whether the specification captures the intended requirements. Finally, the set from where the specification (e.g., safety) can be enforced is explicitly computed and thus conditions for passing control to an emergency controller are clearly defined.
Towards Real-Time Parameter Optimization for Feasible Nonlinear Control with Applications to Robot Locomotion

(Georgia Institute of Technology, 2016-07) Powell, Matthew J. ; Ames, Aaron D.

This paper considers the application of classical control methods, designed for unconstrained nonlinear systems, to systems with nontrivial input constraints. As shown throughout the literature, unconstrained classical methods can be used to stabilize constrained systems, however, (without modification) these unconstrained methods are not guaranteed to work for a general control problem. In this paper, we propose conditions for which classical unconstrained methods can be guaranteed to exponentially stabilize constrained systems – which we term “feasibility” conditions – and we provide examples of how to construct explicitly feasible controllers. The control design methods leverage control Lyapunov functions (CLF) describing the “desired behavior” of the system; and we claim that in the event that a system’s input constraints prevent the production of an exponentially stabilizing input for a particular CLF, a new, locally feasible CLF must be produced. To this end, we propose a novel hybrid feasibility controller consisting of a continuous-time controller which implements a CLF and a discrete parameter update law which finds feasible controller parameters as needed. Simulation results suggest that the proposed method can be used to overcome certain catastrophic infeasibility events encountered in robot locomotion.
Safety Barrier Certificates for Heterogeneous Multi-Robot Systems

(Georgia Institute of Technology, 2016-07) Wang, Li ; Ames, Aaron ; Egerstedt, Magnus B.

This paper presents a formal framework for collision avoidance in multi-robot systems, wherein an existing controller is modified in a minimally invasive fashion to ensure safety. We build this framework through the use of control barrier functions (CBFs) which guarantee forward invariance of a safe set; these yield safety barrier certificates in the context of heterogeneous robot dynamics subject to acceleration bounds. Moreover, safety barrier certificates are extended to a distributed control framework, wherein neighboring agent dynamics are unknown, through local parameter identification. The end result is an optimization-based controller that formally guarantees collision free behavior in heterogeneous multi-agent systems by minimally modifying the desired controller via safety barrier constraints. This formal result is verified in simulation on a multi-robot system consisting of both “sluggish” and “agile” robots.
Realizing Dynamic and Efficient Bipedal Locomotion on the Humanoid Robot DURUS

(Georgia Institute of Technology, 2016-05) Reher, Jacob ; Cousineau, Eric A. ; Hereid, Ayonga ; Hubicki, Christian M. ; Ames, Aaron D.

This paper presents the methodology used to achieve efficient and dynamic walking behaviors on the prototype humanoid robotics platform, DURUS. As a means of providing a hardware platform capable of these behaviors, the design of DURUS combines highly efficient electromechanical components with “control in the loop” design of the leg morphology. Utilizing the final design of DURUS, a formal framework for the generation of dynamic walking gaits which maximizes efficiency by exploiting the full body dynamics of the robot, including the interplay between the passive and active elements, is developed. The gaits generated through this methodology form the basis of the control implementation experimentally realized on DURUS; in particular, the trajectories generated through the formal framework yield a feedforward control input which is modulated by feedback in the form of regulators that compensate for discrepancies between the model and physical system. The end result of the unified approach to control-informed mechanical design, formal gait design and regulator-based feedback control implementation is efficient and dynamic locomotion on the humanoid robot DURUS. In particular, DURUS was able to demonstrate dynamic locomotion at the DRC Finals Endurance Test, walking for just under five hours in a single day, traveling 3.9 km with a mean cost of transport of 1.61-the lowest reported cost of transport achieved on a bipedal humanoid robot.
3D Dynamic Walking with Underactuated Humanoid Robots: A Direct Collocation Framework for Optimizing Hybrid Zero Dynamics

(Georgia Institute of Technology, 2016-05) Hereid, Ayonga ; Cousineau, Eric A. ; Hubick, Christian M. ; Ames, Aaron D.

Hybrid zero dynamics (HZD) has emerged as a popular framework for dynamic and underactuated bipedal walking, but has significant implementation difficulties when applied to the high degrees of freedom present in humanoid robots. The primary impediment is the process of gait design– it is difficult for optimizers to converge on a viable set of virtual constraints defining a gait. This paper presents a methodology that allows for the fast and reliable generation of efficient multi-contact robotic walking gaits through the framework of HZD, even in the presence of underactuation. To achieve this goal, we unify methods from trajectory optimization with the control framework of multi-domain hybrid zero dynamics. By formulating a novel optimization problem in the context of direct collocation and generating analytic Jacobians for the constraints, solving the resulting nonlinear program becomes tractable for large-scale nonlinear programming solvers, even for systems as high-dimensional as humanoid robots. We experimentally validated our methodology on the spring-legged prototype humanoid, DURUS, showing that the optimization approach yields dynamic and stable 3D walking gaits.
Work those Arms: Toward Dynamic and Stable Humanoid Walking that Optimizes Full-Body Motion

(Georgia Institute of Technology, 2016-05) Hubicki, Christian M. ; Hereid, Ayonga ; Grey, Michael X. ; Thomaz, Andrea L. ; Ames, Aaron D.

Humanoid robots are designed with dozens of actuated joints to suit a variety of tasks, but walking controllers rarely make the best use of all of this freedom. We present a framework for maximizing the use of the full humanoid body for the purpose of stable dynamic locomotion, which requires no restriction to a planning template (e.g. LIPM). Using a hybrid zero dynamics (HZD) framework, this approach optimizes a set of outputs which provides requirements for the motion for all actuated links, including arms. These output equations are then rapidly solved by a whole-body inverse-kinematic (IK) solver, providing a set of joint trajectories to the robot. We apply this procedure to a simulation of the humanoid robot, DRC-HUBO, which has over 27 actuators. As a consequence, the resulting gaits swing their arms, not by a user defining swinging motions a priori or superimposing them on gaits post hoc, but as an emergent behavior from optimizing the dynamic gait. We also present preliminary dynamic walking experiments with DRC-HUBO in hardware, thereby building a case that hybrid zero dynamics as augmented by inverse kinematics (HZD+IK) is becoming a viable approach for controlling the full complexity of humanoid locomotion.
Multi-Contact Locomotion on Transfemoral Prostheses via Hybrid System Models and Optimization-Based Control

(Georgia Institute of Technology, 2016-03) Zhao, Huihua ; Horn, Jonathan ; Reher, Jacob ; Paredes, Victor ; Ames, Aaron D.

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 multi-domain hybrid system models and optimization-based controllers to achieve human-like multi-contact prosthetic walking on a custom-built prosthesis: AMPRO. To achieve this goal, unimpaired human locomotion data is collected and the nominal multi-contact human gait is studied. Inspired by previous work which realized multi-contact locomotion on a bipedal robot AMBER2, a hybrid system based optimization problem utilizing the collected reference human gait as reference is utilized to formally design stable multi-contact 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 multi-contact prosthetic walking captures the essentials of natural human walking both kinematically and kinetically.
First Steps Toward Translating Robotic Walking To Prostheses: A Nonlinear Optimization Based Control Approach

(Georgia Institute of Technology, 2016) Zhao, Huihua ; Horn, Jonathan ; Reher, Jacob ; Paredes, Victor ; Ames, Aaron D.

This paper presents the first steps toward successfully translating nonlinear real-time optimization based controllers from bipedal walking robots to a self-contained powered transfemoral prosthesis: AMPRO, with the goal of improving both the tracking performance and the energy efficiency of prostheses control. To achieve this goal, a novel optimal control strategy combining control Lyapunov function (CLF) based quadratic programs (QP) with impedance control is proposed. This optimal controller is first verified on a human-like bipedal robot platform, AMBER. The results indicate improved (compared to variable impedance control) tracking performance, stability and robustness to unknown disturbances. To translate this complete methodology to a prosthetic device with an amputee, 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, i.e., parameterized trajectories, specifically for the amputee and the prosthesis. A online optimization based controller is 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. Importantly, the proposed control law displays remarkable tracking and improved energy efficiency, outperforming PD and impedance control strategies. This is demonstrated experimentally on the prosthesis AMPRO through the implementation of the holistic sensing, algorithm and control framework, with the end result being stable prosthetic walking by an amputee.