Design Optimization, Analysis, and Control of Walking Robots

Passive dynamic walking refers to the dynamical behavior of mechanical devices that are able to naturally walk down a shallow slope in a stable manner, without using actuation or sensing of any kind. Such devices can attain motions that are remarkably human-like by purely exploiting their natural dynamics. This suggests that passive dynamic walking machines can be used to model and study human locomotion; however, there are two major limitations: they can be difficult to design, and they cannot walk on level ground or uphill without some kind of actuation. This thesis presents a mechanism design optimization framework that allows the designer to find the best design parameters based on the chosen performance metric(s). The optimization is formulated as a convex problem, where its solutions are globally optimal and can be obtained efficiently. To enable locomotion on level ground and uphill, this thesis studies a robot based on a passive walker: the rimless wheel with an actuated torso. We design and validate two control policies for the robot through the use of scalable methodology based on tools from mathematical analysis, optimization theory, linear algebra, differential equations, and control theory

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

Data-Driven Design of Energy-Shaping Controllers for Swing-Up Control of Underactuated Robots

We propose a novel data-driven procedure to train a neural network for the swing-up control of underactuated robotic systems. Our approach is inspired by several recent developments ranging from nonlinear control theory to machine learning. We embed a neural network indirectly into the equations of motion of the robotic manipulator as its control input. Using familiar results from passivity-based and energy-shaping control literature, this control function is determined by the appropriate gradients of a neural network, acting as an energy-like (Lyapunov) function. We encode the task of swinging-up robotic systems through the use of transverse coordinates and goal sets; which drastically accelerates the rate of learning by providing a concise target for the neural network. We demonstrate the efficacy of the algorithm with both numerical simulations and experiments

Convex multi-criteria design optimization of robotic manipulators via sum-of-squares programming

This paper presents a general framework for optimization of robotic manipulators via sums-of-squares (SoS) programming (semidefinite convex optimization) with multiple design objectives. Both kinematic and dynamic performance measures are discussed and an optimization problem for a proof-of-concept robotic manipulator has been formulated. SoS programming is shown to promise advantages as it can provide globally optimal results up to machine precision and scales much better with respect to the number of design variables than other methods which can obtain globally optimal solutions

Combining Energy-Shaping Control of Dynamical Systems with Data-Driven Approaches

Machine learning approaches to the problem of control design are flexible, but they demand large databases and computation time for training. Part of this central challenge is due to treating the environment as a black box, ignoring the useful geometric or algebraic structures of the control system. In this work, we propose an efficient data-driven procedure that leverages the known dynamics and techniques from nonlinear control theory in order to design swing-up controllers for underactuated robotic systems. We embed a neural network into the equations of motion of the robotic manipulator through its control input. This control function is determined by the appropriate gradients of a neural network, acting as an energy-like (Lyapunov) function. We encode the swing-up task through the use of transverse coordinates and goal sets; which provides a concise target for the neural network and drastically accelerates the rate of learning. We demonstrate the efficacy and robustness of the algorithm with numerical simulations and experiments on hardware

Robustness of Control Design via Bayesian Learning

In the realm of supervised learning, Bayesian learning has shown robust predictive capabilities under input and parameter perturbations. Inspired by these findings, we demonstrate the robustness properties of Bayesian learning in the control search task. We seek to find a linear controller that stabilizes a one-dimensional open-loop unstable stochastic system. We compare two methods to deduce the controller: the first (deterministic) one assumes perfect knowledge of system parameter and state, the second takes into account uncertainties in both and employs Bayesian learning to compute a posterior distribution for the controller

Robust Data-Driven Passivity-Based Control of Underactuated Systems via Neural Approximators and Bayesian Inference

We synthesize controllers for underactuated robotic systems using data-driven approaches. Inspired by techniques from classical passivity theory, the control law is parametrized by the gradient of an energy-like (Lyapunov) function, which is represented by a neural network. With the control task encoded as the objective of the optimization, we systematically identify the optimal neural net parameters using gradient-based techniques. The proposed method is validated on the cart-pole swing-up task, both in simulation and on a real system. Additionally, we address questions about controller’s robustness against model uncertainties and measurement noise, using a Bayesian approach to infer a probability distribution over the parameters of the controller. The proposed robustness improvement technique is demonstrated on the simple pendulum system

Efficient Singularity-Free Workspace Approximations Using Sum-of-Squares Programming

In this paper, we provide a general framework to determine inner and outer approximations to the singularity-free workspace of fully actuated robotic manipulators, subject to Type-I and Type-II singularities. This framework utilizes the sum-of-squares optimization technique, which is numerically implemented by semidefinite programming. In order to apply the sum-of-squares optimization technique, we convert the trigonometric functions in the kinematics of the manipulator to polynomial functions with an additional constraint. We define two quadratic forms, describing two ellipsoids, whose volumes are optimized to yield inner and outer approximations of the singularity-free workspace