Correct Software Synthesis for Stable Speed-Controlled Robotic Walking

Presented at the 2013 Robotics: Science and Systems Conference VII (RSS), 24-28 June 2013, Berlin, Germany.We present a software synthesis method for speed- controlled robot walking based on supervisory control of a context-free Motion Grammar. First, we use Human-Inspired control to identify parameters for fixed speed walking and for transitions between fixed speeds, guaranteeing dynamic stability. Next, we build a Motion Grammar representing the discrete- time control for this set of speeds. Then, we synthesize C code from this grammar and generate supervisors¹ online to achieve desired walking speeds, guaranteeing correctness of discrete computation. Finally, we demonstrate this approach on the Aldebaran NAO, showing stable walking transitions with dynamically selected speeds

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

Planar Multicontact Locomotion Using Hybrid Zero Dynamics

This thesis proposes a method for generating multi-contact, humanlike locomotion via a human-inspired optimization. The chief objective of this work is to offer an initial solution for obtaining multi-domain walking gaits containing domains with differing degrees of actuation. Motivated by the fact that locomotion inherently includes impacts, a hybrid systems approach is used. Through Lagrangian mechanics, a dynamic model of the system is derived that governs the continuous dynamics, while the dynamics during the impacts are modeled assuming perfectly plastic impacts in which the ground imparts an impulsive force on the impacting link. Using the dynamic model of the planar bipedal robot Amber 2, a seven link biped, a human-inspired optimization is presented which leverages the concept of zero dynamics, allowing for a low dimensional representation of the full order dynamics. Within the optimization, constraints are constructed based on the interaction be- tween the robot and the walking surface that ensure the optimized gait is physically realizable. Other constraints can be used to influence or “shape” the optimized walking gait such as kinematic and/or torque constraints. This optimized walking gait is then realized through the method of Input/Output Linearization. Finally, the utilization of online optimization in the form of a quadratic program increase the capabilities of simple Input/Output Linearization by introducing a notion of optimality as well as the ability to distribute torque as necessary to meet actuator requirements. Ultimately the combination of the flexability of the human-inspired optimization along with the controllers described result in not only multi-domain human-like walking, but even more importantly a tool for rapidly designing new walking gaits

Robot Locomotion Controller Generation Through Human-Inspired Optimization

This thesis presents an approach to the formal design, optimization and implementation of bipedal robotic walking controllers, with experimental application on two biped platforms. Standard rigid-body modeling is used to construct a hybrid sys- tem model of robotic walking; this model estimates the motion of the robot hardware under a given control action. The primary objective of this thesis is the construction of a control law which effects, on the robot, a periodic “walking” behavior. The pro- cess begins with examination of human walking data—specifically outputs of human walking—which provide inspiration for the construction of formal walking control laws. These controllers drive the robot to a low-dimensional representation, termed the partial hybrid zero dynamics, which is shaped by the parameters of the outputs describing the human output data. The main result of this paper is an optimization problem that produces a low-dimensional representation that “best” fits the human data while simultaneously enforcing constraints that ensure a stable periodic orbit and constraints which model the physical limitations of the robot hardware. This formal result is demonstrated through simulation and utilized to obtain 3D walking experimentally with an Aldebaran NAO robot and NASA’s prototype Leg Testbed robot

Trajectory Optimization and Machine Learning to Design Feedback Controllers for Bipedal Robots with Provable Stability

This thesis combines recent advances in trajectory optimization of hybrid dynamical systems with machine learning and geometric control theory to achieve unprecedented performance in bipedal robot locomotion. The work greatly expands the class of robot models for which feedback controllers can be designed with provable stability. The methods are widely applicable beyond bipedal robots, including exoskeletons, and prostheses, and eventually, drones, ADAS, and other highly automated machines. One main idea of this thesis is to greatly expand the use of multiple trajectories in the design of a stabilizing controller. The computation of many trajectories is now feasible due to new optimization tools. The computations are not fast enough to apply in the real-time, however, so they are not feasible for model predictive control (MPC). The offline “library” approach will encounter the curse of dimensionality for the high-dimensional models common in bipedal robots. To overcome these obstructions, we embed a stable walking motion in an attractive low-dimensional surface of the system's state space. The periodic orbit is now an attractor of the low-dimensional state-variable model but is not attractive in the full-order system. We then use the special structure of mechanical models associated with bipedal robots to embed the low-dimensional model in the original model in such a manner that the desired walking motions are locally exponentially stable. The ultimate solution in this thesis will generate model-based feedback controllers for bipedal robots, in such a way that the closed-loop system has a large stability basin, exhibits highly agile, dynamic behavior, and can deal with significant perturbations coming from the environment. In the case of bipeds: “model-based” means that the controller will be designed on the basis of the full floating-base dynamic model of the robot, and not a simplified model, such as the LIP (Linear Inverted Pendulum). By “agile and dynamic” is meant that the robot moves at the speed of a normal human or faster while walking off a curb. By “significant perturbation” is meant a human tripping, and while falling, throwing his/her full weight into the back of the robot.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145992/1/xda_1.pd

From bipedal locomotion to prosthetic walking: A hybrid system and nonlinear control approach

When modeled after the human form, humanoid robots more easily garner societal acceptance and gain increased dexterity in human environments. During this process of humanoid robot design, research on simulated bodies also yields a better understanding of the original biological system. Such advantages make humanoid robots ideal for use in areas such as elderly assistance, physical rehabilitation, assistive exoskeletons, and prosthetic devices. In these applications specifically, an understanding of human-like bipedal robotic locomotion is requisite for practical purposes. However, compared to mobile robots with wheels, humanoid walking robots are complex to design, difficult to balance, and hard to control, resulting in humanoid robots which walk slowly and unnaturally. Despite emerging research and technologies on humanoid robotic locomotion in recent decades, there still lacks a systematic method for obtaining truly kinematic and fluid walking. In this dissertation, we propose a formal optimization framework for achieving stable, human-like robotic walking with natural heel and toe behavior. Importantly, the mathematical construction allows us to directly realize natural walking on the custom-designed physical robot, AMBER2, resulting in a sustainable and robust multi-contact walking gait. As one of the ultimate goals of studying human-like robotic locomotion, the proposed systematic methodology is then translated to achieve prosthetic walking that is both human-like and energy-efficient, with reduced need for parameter tuning. We evaluate this method on two custom, powered transfemoral prostheses in both 2D (AMPRO1) and 3D (AMPRO3) cases. Finally, this dissertation concludes with future research opportunities.Ph.D

Dynamic humanoid locomotion: Hybrid zero dynamics based gait optimization via direct collocation methods

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 dissertation presents a methodology that allows for the fast and reliable generation of efficient multi-domain 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. We present a novel optimization formulation in the context of direct collocation methods and HZD where we rigorously generate analytic Jacobians for the constraints. Two collocation methods, local collocation and pseudospectral (global) collocation, are developed within an unified framework, and their performance in different circumstances is comparatively studied. As a result, solving the resulting nonlinear program becomes tractable for large-scale NLP solvers, even for systems as high-dimensional as humanoid robots. We experimentally validate our methodology on the spring-legged prototype humanoid, DURUS, showing that the optimization approach yields dynamic and stable walking gaits for different walking configurations, including unrestricted 3D dynamic walking.Ph.D

Study and choice of actuation for a walking assist device

International audienceA walking assist device (WAD) with bodyweight support reduces energy expenditure of a walking person. However, it is also important that the location of actuators in the WAD will be optimally chosen. For this purpose a wearable assist device composed of a bodyweight support, legs and shoes articulated with hip (upper joint), knee (middle joint), and ankle (lower joint) is discussed. Since human walk involves large displacements only in sagittal plane, a planar model is considered. In order to evaluate the optimal distribution of input torques, a bipedal model of a seven-link system with several walking velocities is coupled with the mentioned WAD. To study the efficiency of the WAD and to choose an appropriate actuation, the torque cost is evaluated when the same walking pattern are tracked with and without a WAD. The paper deals with the torque cost for the human and the WAD with several types of actuation. It is shown that full actuation with six motors or partial actuation with two motors located at the upper joints are two more efficient solutions while an actuation at the middle joints or lower joints only is ineffective. The numerical simulations carried out for several walking velocities confirm the mentioned observations