Energy And Passivity Based Control For Bipeds And Assistive Walking Devices

Locomotion is inherently an energy regulation challenge; ground impacts deplete the mechanical energy of the walking system with every step. When a person’s leg is amputated, one of the conventional medical devices used to help them recover their mobility is a passive prosthesis. However, this device is incapable of doing positive work on the human body to counteract energy depletion and restore the user’s mechanical energy. Powered prostheses have been developed and researched to address this, but recent control methods have focused on tracking joint trajectories or impedance while ignoring the fundamental kinetic aspect of human locomotion. The prevailing goal of this work is to construct a control method for a powered lower-limb prosthesis that explicitly and directly enhances the kinetics of the combined human-prosthesis system to assist human locomotion. The method proposed to accomplish this utilizes energy and passivity based control techniques to modify the dynamics of the prosthesis. This dissertation develops control theory related to these techniques for autonomous bipedal robots so that they can then be translated onto the target prosthesis system. Specifically, it shows how to use energy shaping and regulation to change characteristics of a walking gait, like walking speed, via switching of a small set of physically meaningful parameters. Experimental results that demonstrate proof-of-concept on a powered knee-ankle prosthetic leg are presented.

Human walking is dynamic, stable, and energy efficient. To achieve such remarkable legged locomotion in robots, engineers have explored bipedal robots developed based on two paradigms: trajectory-controlled and passive-based walking. Trajectory-controlled bipeds often deliver energy-inefficient gaits. The reason is that these bipeds are controlled via high-impedance geared electrical motors to accurately follow predesigned trajectories. Such trajectories are designed to keep a biped locally balanced continually while walking. On the other hand, passive-based bipeds provide energy-efficient gaits. The reason is that these bipeds adapt to their natural dynamics. Such gaits are stable limit-cycles through entire walking motion, and do not require being locally balanced at every instant during walking. However, passive-based bipeds are often of round/point foot bipeds that are not capable of achieving and experiencing standing, stopping, and some important bipedal gait phases and events, such as the double support phase. Therefore, the goals of this thesis are established such that the aforementioned limitations on trajectory-controlled and passive-based bipeds are resolved. Toward the above goal, comprehensive simulation and experimental explorations into bipedal walking have been carried out. Firstly, a novel systematic trajectory-controlled gait-planning framework has been developed to provide mechanical insights into bipedal walking in terms of gait characteristics and energy efficiency. For the same purpose, a novel mathematical model of passive-based bipedal walking with compliant hip-actuation and compliant-ankle flat-foot has been developed. Finally, based on mechanical insights that have been achieved by the aforementioned passive-based model, a physical prototype of a passive-based bipedal robot has been designed and fabricated. The prototype experimentally validates the importance of compliant hip-actuation in achieving a highly dynamic and energy efficient gait.

Abstract: This research focuses on the application of existing design, modeling, and control techniques to study uninvestigated problems in the area of bipedal walking robots. The first portion of this thesis presents a method of integrating mechanism design and hybrid system analysis for the design of a class of single-degree-of-freedom (DOF) planar bipedal robots that can achieve dynamic walking gaits that are stable. These bipeds employ mechanical coordination to reduce the DOF, which can result in a reduction of the complexity of the control strategies needed to enable stable walking. Prior to this work, a methodology for the design of this type of biped had yet to be developed. The second portion of this thesis investigates walking in three-dimensions (3D). A five-DOF, 3D bipedal model is derived and is used to study the degree of dynamic coupling between frontal and sagittal plane motions. Since the dynamics are found to he inherently coupled, a feedback control algorithm that simultaneously accounts for sagittal and frontal plane motions is introduced. With this control, only unstable periodic gaits are obtained. The final portion of this thesis also involves walking in 3D but focuses on the use of a passive-dynamic walker as a basis for the development of 3D controlled bipedal models. The basin of attraction of a known, stable gait for a passive 3D biped is estimated. The stability mechanisms of the limit cycle are also analyzed. Finally, a passivity-based control strategy is introduced that results in a moderate increase in the size of the basin of attraction. Prior to this work, this methodology had yet to be applied to a 3D passive biped.

This thesis presents a hierarchical geometric control approach for fast and energetically efficient bipedal dynamic walking in three-dimensional (3-D) space to enable motion planning applications that have previously been limited to inefficient quasi-static walkers. In order to produce exponentially stable hybrid limit cycles, we exploit system energetics, symmetry, and passivity through the energy-shaping method of controlled geometric reduction. This decouples a subsystem corresponding to a lower-dimensional robot through a passivity-based feedback transformation of the system Lagrangian into a special form of controlled Lagrangian with broken symmetry, which corresponds to an equivalent closed-loop Hamiltonian system with upper-triangular form. The first control term reduces to mechanically-realizable passive feedback that establishes a functional momentum conservation law that controls the "divided" cyclic variables to set-points or periodic orbits. We then prove extensive symmetries in the class of open kinematic chains to present the multistage application of controlled reduction. A reduction-based control law is derived to construct straight-ahead and turning gaits for a 4-DOF and 5-DOF hipped biped in 3-D space, based on the existence of stable hybrid limit cycles in the sagittal plane-of-motion. Given such a set of asymptotically stable gait primitives, a dynamic walker can be controlled as a discrete-time switched system that sequentially composes gait primitives from step to step. We derive "funneling" rules by which a walking path that is a sequence of these gaits may be stably followed by the robot. The primitive set generates a tree exploring the action space for feasible walking paths, where each primitive corresponds to walking along a nominal arc of constant curvature. Therefore, dynamically stable motion planning for dynamic walkers reduces to a discrete search problem, which we demonstrate for 3-D compass-gait bipeds. After reflecting on several connections to human biomechanics, we propose extensions of this energy-shaping control paradigm to robot-assisted locomotor rehabilitation. This work aims to offer a systematic design methodology for assistive control strategies that are amenable to sequential composition for novel progressive training therapies.

Overground walking can be achieved for patients with gait impairments by using the lower limb exoskeleton robots. Since it is a challenge to keep balance for patients with insufficient upper body strength, a robotic walker is necessary to assist with the walking balance. However, since the walking pattern varies over time, controlling the robotic walker to follow the walking of the human-exoskeleton system in coordination is a critical issue. Inappropriate control strategy leads to the unnecessary energy cost of the human-exoskeleton-walker (HEW) system and also results in the bad coordination between the human-exoskeleton system and the robotic walker. In this paper, we proposed a Coordinated Energy-Efficient Control (CEEC) approach for the HEW system, which is based on the extremum seeking control algorithm and the coordinated motion planning strategy. First, the extremum seeking control algorithm is used to find the optimal supporting force of the support joint in real time to maximize the energy efficiency of the human-exoskeleton system. Second, the appropriate reference joint angles for wheels of the robotic walker can be generated by the coordinated motion planning strategy, causing the good coordination between the human-exoskeleton system and the robotic walker. The proposed approach has been tested on the HEW simulation model, and the experimental results indicate that the coordinated energy-efficient walking can be achieved with the proposed approach, which is increased by 60.16% compared to the conventional passive robotic walker.

In the second part, we discuss dynamics and optimality in perturbation rejection using simple mathematical models of human walking and running. We show that energy optimal perturbation recovery predicts features of the control seen previously in human locomotion -- for instance, using appropriate foot placement to redirect the leg force to correct for center of mass state deviations from the nominal. Leg force during stance phase is modulated more in walking than running perturbation recovery. Further, we find that the optimal feedback control is remarkably linear in many variables, suggesting that it may be possible to obtain effective control, large basins of attraction, and near-energy-optimality with relatively simple control architectures. Finally, in the third part, we elaborate on two mechanisms for responding to persistent and periodic perturbations during walking, such as those arising from an assistive device, exoskeleton, or prosthesis. First, we discuss entrainment to perturbations due to the intrinsic stable dynamics of the biped, providing a mathematical framework based on phase response curves. Next, we discuss entrainment to perturbations due to energy optimization, showing how entrainment to some kinds of repeated perturbations can reduce the energy cost of walking. The models, methods, and results in this thesis shed light on how walking and running could be controlled in humans and robots, and has future applications to the design of devices such as exoskeletons and prosthesis.

Two control sampling time selection methods are introduced for digital controllers. A 7-DOF biped is designed and built for experiments. Each joint has its own independent microcontroller-based control system. PD controllers are used to control the biped joints. Simulations are performed for the walking trajectory and zero moment point. Simulation results show that the walking trajectory is stable for the 7-DOF biped. Experiment results indicate that the sampling time is proper and the PID controller works well in both setpoint control and trajectory tracking. The experiment for the marching in place shows the trajectory is stable and the biped can balance during the marching process. Key Words: Biped, cubic Hermite interpolation, zero moment point, trajectory tracking, setpoint sampling time, control sampling time, PID, microcontroller."--Abstract.

Wearable Robotics: Systems and Applications provides a comprehensive overview of the entire field of wearable robotics, including active orthotics (exoskeleton) and active prosthetics for the upper and lower limb and full body. In its two major sections, wearable robotics systems are described from both engineering perspectives and their application in medicine and industry. Systems and applications at various levels of the development cycle are presented, including those that are still under active research and development, systems that are under preliminary or full clinical trials, and those in commercialized products. This book is a great resource for anyone working in this field, including researchers, industry professionals and those who want to use it as a teaching mechanism. Provides a comprehensive overview of the entire field, with both engineering and medical perspectives Helps readers quickly and efficiently design and develop wearable robotics for healthcare applications