160 research outputs found
Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 54).Underactuated robotics, though surrounded by an established body of work, has certain limitations when nonlinear adaptive control principles are applied. This thesis applies a nonlinear adaptative controller that avoids many of these limitations using alterations inspired by the control of a similar underactuated system, the cart-pole. Due to the complexity of the system, a sums-of-squares MATLAB toolbox is used to generate a suitable Lyapunov Candidate used for proofs of stability, with claims of local stability made using Barbalat's Lemma. This provides us with a local domain of attraction for the altered classical nonlinear adaptive controller. In addition, the algorithm known as LQR Trees is applied to the system in order to create a controller with a larger region of attraction and lower torque requirements, though without an adaptive component. Both control systems are implemented in simulations using MATLAB.by Ian Charles Rust.S.B
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
Shaping in Practice: Training Wheels to Learn Fast Hopping Directly in Hardware
Learning instead of designing robot controllers can greatly reduce
engineering effort required, while also emphasizing robustness. Despite
considerable progress in simulation, applying learning directly in hardware is
still challenging, in part due to the necessity to explore potentially unstable
parameters. We explore the concept of shaping the reward landscape with
training wheels: temporary modifications of the physical hardware that
facilitate learning. We demonstrate the concept with a robot leg mounted on a
boom learning to hop fast. This proof of concept embodies typical challenges
such as instability and contact, while being simple enough to empirically map
out and visualize the reward landscape. Based on our results we propose three
criteria for designing effective training wheels for learning in robotics. A
video synopsis can be found at https://youtu.be/6iH5E3LrYh8.Comment: Accepted to the IEEE International Conference on Robotics and
Automation (ICRA) 2018, 6 pages, 6 figure
Data-Driven Passivity-Based Control of Underactuated Robotic Systems
Classical control strategies for robotic systems are based on the idea that feedback control can be used to override the natural dynamics of the machines. Passivity-based control (Pbc) is a branch of nonlinear control theory that follows a similar approach, where the natural dynamics is modified based on the overall energy of the system. This method involves transforming a nonlinear control system, through a suitable control input, into another fictitious system that has desirable stability characteristics. The majority of Pbc techniques require the discovery of a reasonable storage function, which acts as a Lyapunov function candidate that can be used to certify stability.
There are several challenges in the design of a suitable storage function, including: 1) what a reasonable choice for the function is for a given control system, and 2) the control synthesis requires a closed-form solution to a set of nonlinear partial differential equations. The latter is in general difficult to overcome, especially for systems with high degrees of freedom, limiting the applicability of Pbc techniques.
A machine learning framework that automatically determines the storage function for underactuated robotic systems is introduced in this dissertation. This framework combines the expressive power of neural networks with the systematic methods of the Pbc paradigm, bridging the gap between controllers derived from learning algorithms and nonlinear control theory. A series of experiments demonstrates the efficacy and applicability of this framework for a family of underactuated robots
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