Dynamic Modeling of Human Gait Using a Model Predictive Control Approach

This dissertation aims to develop a dynamic model of human gait, especially the working principle of the central nervous system (CNS), using a novel predictive approach. Based on daily experience, it should be straightforward to understand the CNS controls human gait based on predictive control. However, a thorough human gait model using the predictive approach have not yet been explored. This dissertation aims to fill this gap. The development of such a predictive model can assist the developing of lower limb prostheses and orthoses which typically follows a trial and error approach. With the development of the predictive model, lower limb prostheses might be virtually tested so that their performance can be predicted qualitatively, future cost can be reduced, and the risks can be minimized. The model developed in this dissertation includes two parts: a plant model which represents the forward dynamics of human gait and a controller which represents the CNS. The plant model is a seven-segment six-joint model which has nine degrees of freedom. The plant model is validated using data collected from able-bodied human subjects. The experimental moment profile of each joint is input to the model; the kinematic output of the model is consistent with the experimental kinematics which verifies the fidelity of the plant model. The developed predictive human gait model is first validated by simulating able-bodied human gait. The simulation results show that the controller is able to simulate the kinematic output close to experimental data. The developed model was then validated by simulating variable speed able-bodied human gait. The simulation results showed the dynamic characteristics of variable speed gait could be qualitatively predicted by the developed model. Finally the gait of a unilateral transtibial amputee wearing passive prosthetic ankle joint is simulated to verify its ability to qualitatively predict the dynamic characteristics of pathological gait. This dissertation opens the door for modeling human gait from predictive control perspective. With the development of such a model, future prosthetic and orthotic designers can greatly reduce cost, avoid risk, and save time by using the virtual design and testing of prostheses and orthoses

Simulation and Analysis of Walking on Compliant Surfaces

abstract: There are a large group of amputees living in the country and the number of them is supposed to increase a lot in the following years. Among them, lower-limb amputees are the majority. In order to improve the locomotion of lower-limb amputees, many prostheses have been developed. Most commercially available prostheses are passive. They can not actively provide pure torque as an intact human could do. Powered prostheses have been the focus during the past decades. Some advanced prostheses have been successful in walking on level ground as well as on inclined surface and climbing stairs. However, not much work has been done regarding walking on compliant surfaces. My preliminary studies on myoelectric signals of the lower limbs during walking showed that there exists difference in muscle activation when walking on compliant surfaces. However, the mapping of muscle activities to joint torques for a prosthesis that will be capable of providing the required control to walk on compliant surfaces is not straightforward. In order to explore the effects of surface compliance on leg joint torque, a dynamic model of the lower limb was built using Simscape. The simulated walker (android) was commanded to track the same kinematics data of intact human walking on solid surface. Multiple simulations were done while varying ground stiffness in order to see how the torque at the leg joints would change as a function of the ground compliance. The results of this study could be used for the control of powered prostheses for robust walking on compliant surfaces.Dissertation/ThesisMasters Thesis Aerospace Engineering 201

Towards Biomimetic Virtual Constraint Control of a Powered Prosthetic Leg

Abstract-This brief presents a novel control strategy for a powered prosthetic ankle based on a biomimetic virtual constraint. We first derive a kinematic constraint for the "effective shape" of the human ankle-foot complex during locomotion. This shape characterizes ankle motion as a function of the Center of Pressure (COP)-the point on the foot sole where the resultant ground reaction force is imparted. Since the COP moves monotonically from heel to toe during steady walking, we adopt the COP as a mechanical representation of the gait cycle phase in an autonomous feedback controller. We show that our kinematic constraint can be enforced as a virtual constraint by an output linearizing controller that uses only feedback available to sensors onboard a prosthetic leg. Using simulations of a passive walking model with feet, we show that this novel controller exactly enforces the desired effective shape whereas a standard impedance (i.e., proportional-derivative) controller cannot. This work provides a single, biomimetic control law for the entire single-support period during robot-assisted locomotion

Push recovery with stepping strategy based on time-projection control

In this paper, we present a simple control framework for on-line push recovery with dynamic stepping properties. Due to relatively heavy legs in our robot, we need to take swing dynamics into account and thus use a linear model called 3LP which is composed of three pendulums to simulate swing and torso dynamics. Based on 3LP equations, we formulate discrete LQR controllers and use a particular time-projection method to adjust the next footstep location on-line during the motion continuously. This adjustment, which is found based on both pelvis and swing foot tracking errors, naturally takes the swing dynamics into account. Suggested adjustments are added to the Cartesian 3LP gaits and converted to joint-space trajectories through inverse kinematics. Fixed and adaptive foot lift strategies also ensure enough ground clearance in perturbed walking conditions. The proposed structure is robust, yet uses very simple state estimation and basic position tracking. We rely on the physical series elastic actuators to absorb impacts while introducing simple laws to compensate their tracking bias. Extensive experiments demonstrate the functionality of different control blocks and prove the effectiveness of time-projection in extreme push recovery scenarios. We also show self-produced and emergent walking gaits when the robot is subject to continuous dragging forces. These gaits feature dynamic walking robustness due to relatively soft springs in the ankles and avoiding any Zero Moment Point (ZMP) control in our proposed architecture.Comment: 20 pages journal pape

Investigation of Optimization Targets for Predictive Simulation of Human Gait with Model Predictive Control

The design and development of gait-related treatments and devices is inhibited by anabsence of predictive gait models. Understanding of human gait and what motivates walkingpatterns is still limited, despite walking being one of the most routine human activities. While asignificant body of literature exists on gait modeling and optimization criteria to achievesimulated, normal gait, particularly with neuromuscular models, few studies have aimed to applyoptimization targets which approximate metabolic cost to mechanical gait models. Even fewerhave attempted this predictively, with no joint angle data specified a priori. The Sunmodel [31], [32] is one such mechanical framework which utilizes MPC to predict the dynamics ofhuman walking. This thesis expands the Sun model [31], [32] to simulate a full gait cycle (CG) andinvestigates the application of new optimization targets within an existing Model PredictiveControl (MPC) framework for predictive gait simulation developed by Sun [31], [32] .The Sun model [31], [32] was previously limited to a half gait cycle (GC) which assumedbilateral symmetry and optimized only according to characteristic constraints such as step lengthand velocity of the center of mass (COM). In this thesis, the Sun framework and MPC controlscheme were expanded to generate consecutive double support (DS), single support (SS), DS, andSS period simulations, which constitutes a full GC. The resulting GC simulation was not markedby GC events toe off (TO) and heel strike (HS), but did achieve continuity over the period whichwas not achieved by the Sun model [31], [32] . Additionally, new cost functions were developedconsistent with existing literature which suggests that the Central Nervous System (CNS) uses avariety of energy-related targets in generating gait. This thesis demonstrates that the applicationof optimization targets which approximate metabolic costs is possible with the proposed MPCframework for a mechanical gait model, but that the performance of resulting simulations shouldnot be evaluated until a full GC marked by TO and HS is achieved.While a continuous full GC simulation was achieved, the failure of the model to reliablymeet characteristic constraints, particularly in SS, prevents simulation of a GC marked by TO andHS. The work in this thesis points primarily to the failure of the optimization routine within theMPC framework to reliably find a solution that meets constraints as the cause of this problem. Ifthe optimization problem can be classified, an appropriate solution algorithm could be chosenwhich could reliably find a solution for any given set of constraints and initial conditions (IC).Identifying an appropriate solution algorithm could make the MPC framework proposed a viablemethod of gait prediction and simulation.This investigation provides researchers better understanding of the application ofenergy-based optimization in mechanical gait models and the current limitations of gaitprediction and simulation. In addition, direction is given to the future work necessary to establishMPC as a viable control method for gait simulation

Dynamic Modeling, Parameter Estimation and Control of a Leg Prosthesis Test Robot

Robotic testing can facilitate the development of new concepts, designs and control systems for prosthetic limbs. Human subject test clearances, safety and the lack of repeatability associated with human trials can be reduced or eliminated with automated testing, and test modalities are possible which are dangerous or inconvenient to attempt with patients. This paper describes the development, modeling, parameter estimation and control of a robot capable of reproducing two degree-of-freedom hip motion in the sagittal plane. Hip vertical displacement and thigh angle motion profiles are applied to a transfemoral prosthesis attached to the robot. A treadmill is used as walking surface. Aside from tracking hip motion trajectories, the control system can be used to regulate the contact force between the treadmill and the prosthesis. The paper summarizes the overall development process, with emphasis on the generation of a dynamic model that can be used to design closed-loop motion and force control algorithms

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

Determination Of Optimal Counter-Mass Location In Active Prostheses For Transfemoral Amputees To Replicate Normal Swing

Transfemoral amputees suffer the loss of the knee and ankle joints, as well as partial or complete loss of many of the lower extremity muscle groups involved in ambulation. Recent advances in lower limb prostheses have involved the design of active, powered prosthetic knee and ankle-foot components capable of generating knee and ankle torques similar to that of normal gait. The associated onboard motors, conditioning/processing, and battery units of these active components result in increased mass of the respective prosthesis. While not an issue during stance, this increased mass of the prosthesis affects swing. The goal of this study is to develop and validate mathematical models of the transfemoral residual limb and prosthesis, expand these models to include an active ankle-foot, and investigate counter-mass magnitude(s) and location(s) via model optimization that might improve kinematic symmetry during swing. Single- (thigh only, shank only) and multi-segment (combined thigh and shank) optimization of counter-mass magnitudes and locations indicated that a 2.0 kg counter-mass added 8 cm distal and 10 cm posterior to the distal end of knee unit within the shank segment approximated knee kinematics of able-bodied subjects. This location, however, induced artificial hip torques that reduced hip flexion during swing. While such a counter-mass location and magnitude demonstrated theoretical potential, this location is not clinically realistic; mass can only be added within the prosthesis, distal to the residual limb. Clinically realistic counter-masses must also keep the total prosthetic mass to less than 5 kg; greater mass requires supplemental prosthetic suspension, would likely increase energy expenditure during ambulation, and contribute to increased likelihood of fatigue even with active prosthetic components. The ability to simulate the effects of active prosthetic components inclusive of varying placement of battery and signal conditioning units may advance the design of active prostheses that will minimize kinematic asymmetry and result in greater patient acceptance