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

Bio-inspired robotic control in underactuation: principles for energy efficacy, dynamic compliance interactions and adaptability.

Biological systems achieve energy efficient and adaptive behaviours through extensive autologous and exogenous compliant interactions. Active dynamic compliances are created and enhanced from musculoskeletal system (joint-space) to external environment (task-space) amongst the underactuated motions. Underactuated systems with viscoelastic property are similar to these biological systems, in that their self-organisation and overall tasks must be achieved by coordinating the subsystems and dynamically interacting with the environment. One important question to raise is: How can we design control systems to achieve efficient locomotion, while adapt to dynamic conditions as the living systems do? In this thesis, a trajectory planning algorithm is developed for underactuated microrobotic systems with bio-inspired self-propulsion and viscoelastic property to achieve synchronized motion in an energy efficient, adaptive and analysable manner. The geometry of the state space of the systems is explicitly utilized, such that a synchronization of the generalized coordinates is achieved in terms of geometric relations along the desired motion trajectory. As a result, the internal dynamics complexity is sufficiently reduced, the dynamic couplings are explicitly characterised, and then the underactuated dynamics are projected onto a hyper-manifold. Following such a reduction and characterization, we arrive at mappings of system compliance and integrable second-order dynamics with the passive degrees of freedom. As such, the issue of trajectory planning is converted into convenient nonlinear geometric analysis and optimal trajectory parameterization. Solutions of the reduced dynamics and the geometric relations can be obtained through an optimal motion trajectory generator. Theoretical background of the proposed approach is presented with rigorous analysis and developed in detail for a particular example. Experimental studies are conducted to verify the effectiveness of the proposed method. Towards compliance interactions with the environment, accurate modelling or prediction of nonlinear friction forces is a nontrivial whilst challenging task. Frictional instabilities are typically required to be eliminated or compensated through efficiently designed controllers. In this work, a prediction and analysis framework is designed for the self-propelled vibro-driven system, whose locomotion greatly relies on the dynamic interactions with the nonlinear frictions. This thesis proposes a combined physics-based and analytical-based approach, in a manner that non-reversible characteristic for static friction, presliding as well as pure sliding regimes are revealed, and the frictional limit boundaries are identified. Nonlinear dynamic analysis and simulation results demonstrate good captions of experimentally observed frictional characteristics, quenching of friction-induced vibrations and satisfaction of energy requirements. The thesis also performs elaborative studies on trajectory tracking. Control schemes are designed and extended for a class of underactuated systems with concrete considerations on uncertainties and disturbances. They include a collocated partial feedback control scheme, and an adaptive variable structure control scheme with an elaborately designed auxiliary control variable. Generically, adaptive control schemes using neural networks are designed to ensure trajectory tracking. Theoretical background of these methods is presented with rigorous analysis and developed in detail for particular examples. The schemes promote the utilization of linear filters in the control input to improve the system robustness. Asymptotic stability and convergence of time-varying reference trajectories for the system dynamics are shown by means of Lyapunov synthesis