Robust Control Synthesis and Verification for Wire-Borne Underactuated Brachiating Robots Using Sum-of-Squares Optimization

Control of wire-borne underactuated brachiating robots requires a robust feedback control design that can deal with dynamic uncertainties, actuator constraints and unmeasurable states. In this paper, we develop a robust feedback control for brachiating on flexible cables, building on previous work on optimal trajectory generation and time-varying LQR controller design. We propose a novel simplified model for approximation of the flexible cable dynamics, which enables inclusion of parametric model uncertainties in the system. We then use semidefinite programming (SDP) and sum-of-squares (SOS) optimization to synthesize a time-varying feedback control with formal robustness guarantees to account for model uncertainties and unmeasurable states in the system. Through simulation, hardware experiments and comparison with a time-varying LQR controller, it is shown that the proposed robust controller results in relatively large robust backward reachable sets and is able to reliably track a pre-generated optimal trajectory and achieve the desired brachiating motion in the presence of parametric model uncertainties, actuator limits, and unobservable states.Comment: 8 pages, 12 figures, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS

Design, modelling and control of a brachiating power line inspection robot

The inspection of power lines and associated hardware is vital to ensuring the reliability of the transmission and distribution network. The repetitive nature of the inspection tasks present a unique opportunity for the introduction of robotic platforms, which offer the ability to perform more systematic and detailed inspection than traditional methods. This lends itself to improved asset management automation, cost-effectiveness and safety for the operating crew. This dissertation presents the development of a prototype industrial brachiating robot. The robot is mechanically simple and capable of dynamically negotiating obstacles by brachiating. This is an improvement over current robotic platforms, which employ slow, high power static schemes for obstacle negotiation. Mathematical models of the robot were derived to understand the underlying dynamics of the system. These models were then used in the generation of optimal trajectories, using nonlinear optimisation techniques, for brachiating past line hardware. A physical robot was designed and manufactured to validate the brachiation manoeuvre. The robot was designed following classic mechanical design principles, with emphasis on functional design and robustness. System identification was used to capture the plant uncertainty and a feedback controller was designed to track the reference trajectory allowing for energy optimal brachiation swings. Finally, the robot was tested, starting with sub-system testing and ending with testing of a brachiation manoeuvre proving the prospective viability of the robot in an industrial environment

Dynamic Modeling, Design and Control of Wire-Borne Underactuated Brachiating Robots: Theory and Application

The ability of mobile robots to locomote safely in unstructured environments will be a cornerstone of robotics of the future. Introducing robots into fully unstructured environments is known to be a notoriously difficult problem in the robotics field. As a result, many of today's mobile robots are confined to prepared level surfaces in laboratory settings or relatively controlled environments only. One avenue for deploying mobile robots into unstructured settings is to utilize elevated wire networks. The research conducted under this thesis lays the groundwork for developing a new class of wire-borne underactuated robots that employs brachiation -- swinging like an ape -- as a means of locomotion on flexible cables. Executing safe brachiation maneuvers with a cable-suspended underactuated robot is a challenging problem due to the complications induced by the cable dynamics and vibrations. This thesis studies, from concept through experiments, the dynamic modeling techniques and control algorithms for wire-borne underactuated brachiating robots, to develop advanced locomotion strategies that enable the robots to perform energy-efficient and robust brachiation motions on flexible cables. High-fidelity and approximate dynamic models are derived for the robot-cable system, which provide the ability to model the interactions between the cable and the robot and to include the flexible cable dynamics in the control design. An optimal trajectory generation framework is presented in which the flexible cable dynamics are explicitly accounted for when designing the optimal swing trajectories. By employing a variety of control-theoretic methods such as robust and adaptive estimation, control Lyapunov and barrier functions, semidefinite programming and sum-of-squares optimization, a set of closed-loop control algorithms are proposed. A novel hardware brachiating robot design and embodiment are presented, which incorporate unique mechanical design features and provide a reliable testbed for experimental validation of the wire-borne underactuated brachiating robots. Extensive simulation results and hardware experiments demonstrate that the proposed multi-body dynamic models, trajectory optimization frameworks, and feedback control algorithms prove highly useful in real world settings and achieve reliable brachiation performance in the presence of uncertainties, disturbances, actuator limits and safety constraints.Ph.D