MATLAB-based Tools for Modelling and Control of Underactuated Mechanical Systems

Underactuated systems, defined as nonlinear mechanical systems with fewer control inputs than degrees of freedom, appear in a broad range of applications including robotics, aerospace, marine and locomotive systems. Studying the complex low-order nonlinear dynamics of appropriate benchmark underactuated systems often enables us to gain insight into the principles of modelling and control of advanced, higher-order underactuated systems. Such benchmarks include the Acrobot, Pendubot and the reaction (inertia) wheel pendulum. The aim of this paper is to introduce novel MATLAB-based tools which were developed to provide complex software support for modelling and control of these three benchmark systems. The presented tools include a Simulink block library, a set of demo simulation schemes and several innovative functions for mathematical and simulation model generation

Adaptive swing-up and balancing control of acrobot systems

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. 22).The field of underactuated robotics has become the core of agile mobile robotics research. Significant past effort has been put into understanding the swing-up control of the acrobot system. This thesis implements an online, adaptive swing-up and balancing controller with no previous knowledge of the system's mass or geometric parameters. A least squares method is used to identify the 5 parameters necessary to completely characterize acrobot dynamics. Swing up is accomplished using partial feedback linearization and a pump up strategy to add energy to the system. The controller then catches the swung up system in the basin of attraction of an LQR controller computed using the estimated parameter values generated from online system identification. These results are then simulated using a MATLAB simulation environment.by Luke B. Johnson.S.B

Stabilization of the Acrobot via sampled-data passivity-based control

The paper deals with the sampled-data asymptotic stabilization of the Acrobot at its upward equilibrium. The proposed controller results from the action of an Input-Hamiltonian-Matching (IHM) strategy that shapes the closed-loop energy combined with a Damping Injection (DI) feedback designed on the sampled-data equivalent model. Simulations show the effectiveness of the proposed controller

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

Empowerment for Continuous Agent-Environment Systems

This paper develops generalizations of empowerment to continuous states. Empowerment is a recently introduced information-theoretic quantity motivated by hypotheses about the efficiency of the sensorimotor loop in biological organisms, but also from considerations stemming from curiosity-driven learning. Empowemerment measures, for agent-environment systems with stochastic transitions, how much influence an agent has on its environment, but only that influence that can be sensed by the agent sensors. It is an information-theoretic generalization of joint controllability (influence on environment) and observability (measurement by sensors) of the environment by the agent, both controllability and observability being usually defined in control theory as the dimensionality of the control/observation spaces. Earlier work has shown that empowerment has various interesting and relevant properties, e.g., it allows us to identify salient states using only the dynamics, and it can act as intrinsic reward without requiring an external reward. However, in this previous work empowerment was limited to the case of small-scale and discrete domains and furthermore state transition probabilities were assumed to be known. The goal of this paper is to extend empowerment to the significantly more important and relevant case of continuous vector-valued state spaces and initially unknown state transition probabilities. The continuous state space is addressed by Monte-Carlo approximation; the unknown transitions are addressed by model learning and prediction for which we apply Gaussian processes regression with iterated forecasting. In a number of well-known continuous control tasks we examine the dynamics induced by empowerment and include an application to exploration and online model learning

Design and control of a planar two-link manipulator for educational use

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.Cataloged from PDF version of thesis.Includes bibliographical references (p. [19]).This paper proposes a new robotic planar two-link manipulator design for educational use. Planar two-link manipulators are among the most accessible two-degree-of-freedom robots for students because they function like human arms. As a result they are ideal for laboratory teaching environments. While previous designs using belt-driven arms served adequately, this new design possesses a number of features that were not possible with the previous design, including more intuitive simplified dynamics, an expanded workspace allowing multiple full rotations, and the ability to be easily reconfigured into an acrobot (an underactuated double-pendulum which can be stabilized in a vertical configuration while being actuated only at the middle joint). The governing equations of the system are derived and an analysis of velocity control in the xy plane is perform and a control methodology is also presented by which the arm can be stabilized vertically while in its acrobot configuration. A Discussion of tradeoffs relevant to the future design of similar systems is also presented.by David C. Schafer.S.B

Quotient method for controlling the acrobot

This paper describes a two-sweep control design method to stabilize the acrobot, an input-affine under-actuated system, at the upper equilibrium point. In the forward sweep, the system is successively reduced, one dimension at a time, until a two-dimensional system is obtained. At each step of the reduction process, a quotient is taken along one-dimensional integral manifolds of the input vector field. This decomposes the current manifold into classes of equivalence that constitute a quotient manifold of reduced dimension. The input to a given step becomes the representative of the previous-step equivalence class, and a new input vector field can be defined on the tangent of the quotient manifold. The representatives remain undefined throughout the forward sweep. During the backward sweep, the controller is designed recursively, starting with the two- dimensional system. At each step of the recursion, a well-chosen representative of the equivalence class ahead of the current level of recursion is chosen, so as to guarantee stability of the current step. Therefore, this stabilizes the global system once the backward sweep is complete. Although stability can only be guaranteed locally around the upper equilibrium point, the domain of attraction can be enlarged to include the lower equilibrium point, thereby allowing a swing-up implementation. As a result, the controller does not require switching, which is illustrated in simulation. The controller has four tuning parameters, which helps shape the closed-loop behavior