Dynamic balancing of underactuated robots

This thesis presents the control of planar underactuated systems that have one less control input than the number of degrees of freedom. The underactuated robots are studied to achieve dynamically stable motions commonly encountered during robot locomotion. This work emphasizes the relation between the underactuated systems and biped locomotion and builds on the previous works in the literature on underactuated robot locomotion. Two planar system models are treated: an acrobatic robot and a compass biped with torso. The dynamic stability of fast periodic trajectories of these systems are regulated by designing asymptotically stable feedback controllers. The resulting internal dynamics of the systems are analyzed and shaped to achieve energy efficiency and robustness of the closed-loop system trajectories. In particular, Bézier polynomial approximations and parameter optimization methods are used to systematically construct the internal dynamics of the systems. Simulation results are presented for dynamically stable orbits of the acrobatic robot and the compass biped with torso

Robust compound control of dynamic bipedal robots

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior

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

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

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

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

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