Energy Shaping of Underactuated Systems via Interconnection and Damping Assignment Passivity-Based Control with Applications to Planar Biped Robots

The sought goal of this thesis is to show that total energy shaping is an effective and versatile tool to control underactuated mechanical systems. The performance of several approaches, rooted in the port-Hamiltonian formalism, are analyzed while tackling distinct control problems: i) equilibrium stabilization; ii) gait generation; iii) gait robustication. Firstly, a constructive solution to deal with interconnection and damping assignment passivity-based control (IDA-PBC) for underactuated two-degree-of-freedom mechanical systems is proposed. This strategy does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalized momenta are introduced by the controller. The methodology is applied to the stabilization of a translational oscillator with a rotational actuator system, as well as, to the gait generation for an underactuated compass-like biped robot (CBR). Then, the problem of gait generation is addressed using dissipative forces in the controller. In this sense, three distinct controllers are presented, namely simultaneous interconnection and damping assignment passivity-based control with dissipative forces, energy pumping-and-damping passivity-based control (EPD-PBC), and energy pumping-or-damping control. Finally, EPD-PBC is used to increase the robustness of the gait exhibited by the CBR over uncertainties on the initial conditions. The passivity of the system is exploited, as well as, its hybrid nature (using the hybrid zero dynamics method) to carry out the stability analysis. Besides, such an approach is applied to new gaits that are generated using IDA-PBC. Numerical case studies, comparisons, and critical discussions evaluate the performance of the proposed approaches

A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs

This paper presents a passivity-based control strategy dealing with underactuated two-degree-of-freedom (2-DoF) mechanical systems. Such a methodology, which is based on the interconnection and damping assignment passivity-based control (IDA-PBC), rooted within the port-controlled Hamiltonian framework, can be applied to a very large class of underactuated 2-DoF mechanical systems. The main contribution, compared to the previous literature, is that the new methodology does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalised momenta are introduced by the controller. The proposed strategy is applied to two case studies: a) the stabilisation of a translational oscillator with a rotational actuator (TORA) system; b) the gait generation for an underactuated compass-like biped robot. The performances of the presented solution are evaluated through numerical simulations

Interconnection and Damping Assignment Passivity-Based Control for Gait Generation in Underactuated Compass-Like Robots

A compass-like biped robot can go down a gentle slope without the need of actuation through a proper choice of its dynamic parameter and starting from a suitable initial condition. Addition of control actions is requested to generate additional gaits and robustify the existing one. This paper designs an interconnection and damping assignment passivity- based control, rooted within the port-Hamiltonian framework, to generate further gaits with respect to state-of-the-art methodologies, enlarge the basin of attraction of existing gaits, and further robustify the system against controller discretization and parametric uncertainties. The performance of the proposed algorithm is validated through numerical simulations and comparison with existing passivity-based techniques

Energy pumping-and-damping for gait robustification of underactuated planar biped robots within the hybrid zero dynamics framework

This paper addresses the robust gait control for planar and passive biped robots using approaches based on energy properties. Energy pumping-and-damping passivity-based control is used to increase the robustness against uncertainties on the initial conditions of the passive gait exhibited by planar biped robots. The stability analysis is carried out by exploiting the system’s passivity and the hybrid zero dynamics method. Besides, the proposed approach is applied to new gaits that are generated using interconnection and damping assignment passivity-based control. The performance of the proposed design is evaluated through numerical simulations and compared with an existing technique

Control of the TORA System through the IDA-PBC without Explicit Solution of Matching Equations

This paper presents the control of a translational oscillator with a rotational actuator (TORA) system, in full gravity, through the interconnection and damping assignment passivity-based control (IDA-PBC). The sought goal is to control the underactuated TORA system while reducing the complexity in solving the partial differential equations coming out from the so-called matching equations, which arise from the IDA-PBC. The performance of the designed controller is illustrated through numerical simulations