Accurate Step Length Control Strategies for Underactuated and Realistic Series Elastic Actuated Hoppers via High Order PFL

Among the different types of legged robots, hopping robots, aka hoppers, can be classified as one of the simplest sufficient models that capture the important features encompassed in dynamic locomotion: underactuation, compliance, and hybrid features. There is an abundance of work regarding the implementation of highly simplified hopper models, the prevalent example being the spring loaded inverted pendulum (SLIP) model, with the hopes of extracting fundamental control ideas for running and hopping robots. However, real world systems cannot be fully described by such simple models, as real actuators have their own dynamics including additional inertia and non-linear frictional losses. Additionally, implementing feedback control for hopping systems with significant amounts of compliance is difficult as the input variable does not instantaneously change the leg length acceleration. The current state-of-the-art of step length control in the presence of non-steady state motions required for foothold placement is not precise enough for operation in the real world. Therefore, an important step towards demonstrating high controllability and robustness to real-world elements is in providing accurate higher order models of real-world hopper dynamics, along with compatible control strategies. Our modeling work is based on a series-elastic actuated (SEA) hopping robot prototype constructed by our lab group, and we provide verifying hardware results that high order partial feedback linearization (HOPFL) can be implemented directly on the leg state of the robot. Using HOPFL, we investigate two paths of compatible trajectory generation that can accomplish desirable tasks such as precise foothold planning. We investigate the practicality of using SLIP-based trajectory generation techniques on more realistic hopping robots, and show that by implementing HOPFL directly on the robot's leg, we can make use of computationally fast SLIP-based approximations, account for non-trivial pitch dynamics, and improve the state-of-the-art of precision step length control for SEA hoppers. We also consider control strategies towards hoppers for which SLIP-based trajectories may not be compatible, by planning all ground reaction force vector (GRF) components during the stance phase concurrently, using a lower order and very general model to construct trajectories for the system's center of mass (CoM), and maintain body stability by controlling the orientation of the GRF directly. While not purely analytical as our SLIP-based approaches, this method is general enough to work on a variety of hopping robots that are not necessarily kinematically structured resembling the classical SLIP model

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

Systematic Controller Design for Dynamic 3D Bipedal Robot Walking.

Virtual constraints and hybrid zero dynamics (HZD) have emerged as a powerful framework for controlling bipedal robot locomotion, as evidenced by the robust, energetically efficient, and natural-looking walking and running gaits achieved by planar robots such as Rabbit, ERNIE, and MABEL. However, the extension to 3D robots is more subtle, as the choice of virtual constraints has a deciding effect on the stability of a periodic orbit. Furthermore, previous methods did not provide a systematic means of designing virtual constraints to ensure stability. This thesis makes both experimental and theoretical contributions to the control of underactuated 3D bipedal robots. On the experimental side, we present the first realization of dynamic 3D walking using virtual constraints. The experimental success is achieved by augmenting a robust planar walking gait with a novel virtual constraint for the lateral swing hip angle. The resulting controller is tested in the laboratory on a human-scale bipedal robot (MARLO) and demonstrated to stabilize the lateral motion for unassisted 3D walking at approximately 1 m/s. MARLO is one of only two known robots to walk in 3D with stilt-like feet. On the theoretical side, we introduce a method to systematically tune a given choice of virtual constraints in order to stabilize a periodic orbit of a hybrid system. We demonstrate the method to stabilize a walking gait for MARLO, and show that the optimized controller leads to improved lateral control compared to the nominal virtual constraints. We also describe several extensions of the basic method, allowing the use of a restricted Poincaré map and the incorporation of disturbance rejection metrics in the optimization. Together, these methods comprise an important contribution to the theory of HZD.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113370/1/bgbuss_1.pd

Hopping, Landing, and Balancing with Springs

This work investigates the interaction of a planar double pendulum robot and springs, where the lower body (the leg) has been modified to include a spring-loaded passive prismatic joint. The thesis explores the mechanical advantage of adding a spring to the robot in hopping, landing, and balancing activities by formulating the motion problem as a boundary value problem; and also provides a control strategy for such scenarios. It also analyses the robustness of the developed controller to uncertain spring parameters, and an observer solution is provided to estimate these parameters while the robot is performing a tracking task. Finally, it shows a study of how well IMUs perform in bouncing conditions, which is critical for the proper operation of a hopping robot or a running-legged one

Instantaneous Momentum-Based Control of Floating Base Systems

In the last two decades a growing number of robotic applications such as autonomous drones, wheeled robots and industrial manipulators started to be employed in several human environments. However, these machines often possess limited locomotion and/or manipulation capabilities, thus reducing the number of achievable tasks and increasing the complexity of robot-environment interaction. Augmenting robots locomotion and manipulation abilities is a fundamental research topic, with a view to enhance robots participation in complex tasks involving safe interaction and cooperation with humans. To this purpose, humanoid robots, aerial manipulators and the novel design of flying humanoid robots are among the most promising platforms researchers are studying in the attempt to remove the existing technological barriers. These robots are often modeled as floating base systems, and have lost the assumption -- typical of fixed base robots -- of having one link always attached to the ground. From the robot control side, contact forces regulation revealed to be fundamental for the execution of interaction tasks. Contact forces can be influenced by directly controlling the robot's momentum rate of change, and this fact gives rise to several momentum-based control strategies. Nevertheless, effective design of force and torque controllers still remains a complex challenge. The variability of sensor load during interaction, the inaccuracy of the force/torque sensing technology and the inherent nonlinearities of robot models are only a few complexities impairing efficient robot force control. This research project focuses on the design of balancing and flight controllers for floating base robots interacting with the surrounding environment. More specifically, the research is built upon the state-of-the-art of momentum-based controllers and applied to three robotic platforms: the humanoid robot iCub, the aerial manipulator OTHex and the jet-powered humanoid robot iRonCub. The project enforces the existing literature with both theoretical and experimental results, aimed at achieving high robot performances and improved stability and robustness, in presence of different physical robot-environment interactions

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

Reduced Order Model Inspired Robotic Bipedal Walking: A Step-to-step Dynamics Approximation based Approach

Controlling bipedal robotic walking is a challenging task. The dynamics is hybrid, nonlinear, high-dimensional, and typically underactuated. Complex physical constraints have to be satisfied in the walking generation. The stability in terms of not-falling is also hard to be encoded in the walking synthesis. Canonical approaches for enabling robotic walking typically rely on large-scale trajectory optimizations for generating optimal periodic behaviors on the full-dimensional model of the system; then the stabilities of the controlled behaviors are analyzed through the numerically derived Poincaré maps. This full-dimensional periodic behavior based synthesis, despite being theoretically rigorous, suffers from several disadvantages. The trajectory optimization problem is computationally challenging to solve. Non-trivial expert-tuning is required on the cost, constraints, and initial conditions to avoid infeasibilities and local optimality. It is cumbersome for realizing non-periodical behaviors, and the synthesized walking can be sensitive to model uncertainties. In this thesis, we propose an alternative approach of walking synthesis that is based on reduced order modeling and dynamics approximation. We formulate a discrete step-to-step (S2S) dynamics of walking, where the step size is treated as the control input to stabilize the pre-impact horizontal center of mass (COM) state of the robot. Stepping planning thus is converted into a feedback control problem. To effectively and efficiently solve this feedback stepping planning problem, an underactuated Hybrid Linear Inverted Pendulum (H-LIP) model is proposed to approximate the dynamics of underactuated bipedal walking; the linear S2S dynamics of the H-LIP then approximates the robot S2S dynamics. The H-LIP based stepping controller is hence utilized to plan the desired step sizes on the robot to control its pre-impact horizontal COM state. Stable walking behaviors are consequently generating by realizing the desired step size in the output construction and stabilizing the output via optimization-based controllers. We evaluate this approach successfully on several bipedal walking systems with an increase in the system complexity: a planar five-linkage walker AMBER, an actuated version of the Spring Loaded Inverted Pendulum (aSLIP) in both 2D and 3D, and finally the 3D underactuated robot Cassie. The generated dynamic walking behaviors on these systems are shown to be highly versatile and robust. Furthermore, we show that this approach can be effectively extended to realizing more complex walking tasks such as global trajectory tracking and walking on rough terrain.</p