Feedback Control of an Exoskeleton for Paraplegics: Toward Robustly Stable Hands-free Dynamic Walking

This manuscript presents control of a high-DOF fully actuated lower-limb exoskeleton for paraplegic individuals. The key novelty is the ability for the user to walk without the use of crutches or other external means of stabilization. We harness the power of modern optimization techniques and supervised machine learning to develop a smooth feedback control policy that provides robust velocity regulation and perturbation rejection. Preliminary evaluation of the stability and robustness of the proposed approach is demonstrated through the Gazebo simulation environment. In addition, preliminary experimental results with (complete) paraplegic individuals are included for the previous version of the controller.Comment: Submitted to IEEE Control System Magazine. This version addresses reviewers' concerns about the robustness of the algorithm and the motivation for using such exoskeleton

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

Control Implementation of Dynamic Locomotion on Compliant, Underactuated, Force-Controlled Legged Robots with Non-Anthropomorphic Design

The control of locomotion on legged robots traditionally involves a robot that takes a standard legged form, such as the anthropomorphic humanoid, the dog-like quadruped, or the bird-like biped. Additionally, these systems will often be actuated with position-controlled servos or series-elastic actuators that are connected through rigid links. This work investigates the control implementation of dynamic, force-controlled locomotion on a family of legged systems that significantly deviate from these classic paradigms by incorporating modern, state-of-the-art proprioceptive actuators on uniquely configured compliant legs that do not closely resemble those found in nature. The results of this work can be used to better inform how to implement controllers on legged systems without stiff, position-controlled actuators, and also provide insight on how intelligently designed mechanical features can potentially simplify the control of complex, nonlinear dynamical systems like legged robots. To this end, this work presents the approach to control for a family of non-anthropomorphic bipedal robotic systems which are developed both in simulation and with physical hardware. The first is the Non-Anthropomorphic Biped, Version 1 (NABi-1) that features position-controlled joints along with a compliant foot element on a minimally actuated leg, and is controlled using simple open-loop trajectories based on the Zero Moment Point. The second system is the second version of the non-anthropomorphic biped (NABi-2) which utilizes the proprioceptive Back-drivable Electromagnetic Actuator for Robotics (BEAR) modules for actuation and fully realizes feedback-based force controlled locomotion. These systems are used to highlight both the strengths and weaknesses of utilizing proprioceptive actuation in systems, and suggest the tradeoffs that are made when using force control for dynamic locomotion. These systems also present case studies for different approaches to system design when it comes to bipedal legged robots

Motion Planning and Control for the Locomotion of Humanoid Robot

This thesis aims to contribute on the motion planning and control problem of the locomotion of humanoid robots. For the motion planning, various methods were proposed in different levels of model dependence. First, a model free approach was proposed which utilizes linear regression to estimate the relationship between foot placement and moving velocity. The data-based feature makes it quite robust to handle modeling error and external disturbance. As a generic control philosophy, it can be applied to various robots with different gaits. To reduce the risk of collecting experimental data of model-free method, based on the simplified linear inverted pendulum model, the classic planning method of model predictive control was explored to optimize CoM trajectory with predefined foot placements or optimize them two together with respect to the ZMP constraint. Along with elaborately designed re-planning algorithm and sparse discretization of trajectories, it is fast enough to run in real time and robust enough to resist external disturbance. Thereafter, nonlinear models are utilized for motion planning by performing forward simulation iteratively following the multiple shooting method. A walking pattern is predefined to fix most of the degrees of the robot, and only one decision variable, foot placement, is left in one motion plane and therefore able to be solved in milliseconds which is sufficient to run in real time. In order to track the planned trajectories and prevent the robot from falling over, diverse control strategies were proposed according to the types of joint actuators. CoM stabilizer was designed for the robots with position-controlled joints while quasi-static Cartesian impedance control and optimization-based full body torque control were implemented for the robots with torque-controlled joints. Various scenarios were set up to demonstrate the feasibility and robustness of the proposed approaches, like walking on uneven terrain, walking with narrow feet or straight leg, push recovery and so on

Design and development of a hominid robot with local control in its adaptable feet to enhance locomotion capabilities

With increasing mechanization of our daily lives, the expectations and demands in robotic systems increase in the general public and in scientists alike. In recent events such as the Deepwater Horizon''-accident or the nuclear disaster at Fukushima, mobile robotic systems were used, e.g., to support local task forces by gaining visual material to allow an analysis of the situation. Especially the Fukushima example shows that the robotic systems not only have to face a variety of different tasks during operation but also have to deal with different demands regarding the robot's mobility characteristics. To be able to cope with future requirements, it seems necessary to develop kinematically complex systems that feature several different operating modes. That is where this thesis comes in: A robotic system is developed, whose morphology is oriented on chimpanzees and which has the possibility due to its electro-mechanical structure and the degrees of freedom in its arms and legs to walk with different gaits in different postures. For the proposed robot, the chimpanzee was chosen as a model, since these animals show a multitude of different gaits in nature. A quadrupedal gait like crawl allows the robot to traverse safely and stable over rough terrain. A change into the humanoid, bipedal posture enables the robot to move in man-made environments. The structures, which are necessary to ensure an effective and stable locomotion in these two poses, e.g., the feet, are presented in more detail within the thesis. This includes the biological model and an abstraction to allow a technical implementation. In addition, biological spines are analyzed and the development of an active, artificial spine for the robotic system is described. These additional degrees of freedom can increase the robot's locomotion and manipulation capabilities and even allow to show movements, which are not possible without a spine. Unfortunately, the benefits of using an artificial spine in robotic systems are nowadays still neglected, due to the increased complexity of system design and control. To be able to control such a kinematically complex system, a multitude of sensors is installed within the robot's structures. By placing evaluation electronics close by, a local and decentralized preprocessing is realized. Due to this preprocessing is it possible to realize behaviors on the lowest level of robot control: in this thesis it is exemplarily demonstrated by a local controller in the robot's lower leg. In addition to the development and evaluation of robot's structures, the functionality of the overall system is analyzed in different environments. This includes the presentation of detailed data to show the advantages and disadvantages of the local controller. The robot can change its posture independently from a quadrupedal into a bipedal stance and the other way around without external assistance. Once the robot stands upright, it is to investigate to what extent the quadrupedal walking pattern and control structures (like the local controller) have to be modified to contribute to the bipedal walking as well

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

Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters