Model learning for trajectory tracking of robot manipulators

Abstract Model based controllers have drastically improved robot performance, increasing task accuracy while reducing control effort. Nevertheless, all this was realized with a very strong assumption: the exact knowledge of the physical properties of both the robot and the environment that surrounds it. This assertion is often misleading: in fact modern robots are modeled in a very approximate way and, more important, the environment is almost never static and completely known. Also for systems very simple, such as robot manipulators, these assumptions are still too strong and must be relaxed. Many methods were developed which, exploiting previous experiences, are able to refine the nominal model: from classic identification techniques to more modern machine learning based approaches. Indeed, the topic of this thesis is the investigation of these data driven techniques in the context of robot control for trajectory tracking. In the first two chapters, preliminary knowledge is provided on both model based controllers, used in robotics to assure precise trajectory tracking, and model learning techniques. In the following three chapters, are presented the novelties introduced by the author in this context with respect to the state of the art: three works with the same premise (an inaccurate system modeling), an identical goal (accurate trajectory tracking control) but with small differences according to the specific platform of application (fully actuated, underactuated, redundant robots). In all the considered architectures, an online learning scheme has been introduced to correct the nominal feedback linearization control law. Indeed, the method has been primarily introduced in the literature to cope with fully actuated systems, showing its efficacy in the accurate tracking of joint space trajectories also with an inaccurate dynamic model. The main novelty of the technique was the use of only kinematics information, instead of torque measurements (in general very noisy), to online retrieve and compensate the dynamic mismatches. After that the method has been extended to underactuated robots. This new architecture was composed by an online learning correction of the controller, acting on the actuated part of the system (the nominal partial feedback linearization), and an offline planning phase, required to realize a dynamically feasible trajectory also for the zero dynamics of the system. The scheme was iterative: after each trial, according to the collected information, both the phases were improved and then repeated until the task achievement. Also in this case the method showed its capability, both in numerical simulations and on real experiments on a robotics platform. Eventually the method has been applied to redundant systems: differently from before, in this context the task consisted in the accurate tracking of a Cartesian end effector trajectory. In principle very similar to the fully actuated case, the presence of redundancy slowed down drastically the learning machinery convergence, worsening the performance. In order to cope with this, a redundancy resolution was proposed that, exploiting an approximation of the learning algorithm (Gaussian process regression), allowed to locally maximize the information and so select the most convenient self motion for the system; moreover, all of this was realized with just the resolution of a quadratic programming problem. Also in this case the method showed its performance, realizing an accurate online tracking while reducing both the control effort and the joints velocity, obtaining so a natural behaviour. The thesis concludes with summary considerations on the proposed approach and with possible future directions of research

Realtime State Estimation with Tactile and Visual sensing. Application to Planar Manipulation

Accurate and robust object state estimation enables successful object manipulation. Visual sensing is widely used to estimate object poses. However, in a cluttered scene or in a tight workspace, the robot's end-effector often occludes the object from the visual sensor. The robot then loses visual feedback and must fall back on open-loop execution. In this paper, we integrate both tactile and visual input using a framework for solving the SLAM problem, incremental smoothing and mapping (iSAM), to provide a fast and flexible solution. Visual sensing provides global pose information but is noisy in general, whereas contact sensing is local, but its measurements are more accurate relative to the end-effector. By combining them, we aim to exploit their advantages and overcome their limitations. We explore the technique in the context of a pusher-slider system. We adapt iSAM's measurement cost and motion cost to the pushing scenario, and use an instrumented setup to evaluate the estimation quality with different object shapes, on different surface materials, and under different contact modes

On-line Joint Limit Avoidance for Torque Controlled Robots by Joint Space Parametrization

This paper proposes control laws ensuring the stabilization of a time-varying desired joint trajectory, as well as joint limit avoidance, in the case of fully-actuated manipulators. The key idea is to perform a parametrization of the feasible joint space in terms of exogenous states. It follows that the control of these states allows for joint limit avoidance. One of the main outcomes of this paper is that position terms in control laws are replaced by parametrized terms, where joint limits must be avoided. Stability and convergence of time-varying reference trajectories obtained with the proposed method are demonstrated to be in the sense of Lyapunov. The introduced control laws are verified by carrying out experiments on two degrees-of-freedom of the humanoid robot iCub.Comment: 8 pages, 4 figures. Submitted to the 2016 IEEE-RAS International Conference on Humanoid Robot

Design and Development of a High-Performance Quadrotor Control Architecture Based on Feedback Linearization

The purpose of this thesis is to outline the development of a high-performance quadrotor control system for an AscTec Hummingbird quadrotor using direct motor speed control within a Vicon motion capture system environment. A Ground Control Station (GCS) acts as a user interface for selecting flight patterns and displaying sensor values. An on-board Intel Edison embedded Linux computer acts as the quadrotor\u27s controller. The Vicon system measures the quadrotor\u27s position and orientation, while the Hummingbird\u27s stock AscTec Autopilot board provides inertial measurements and receives motor speed commands. Based on the flight pattern set by the GCS, smooth and di erentiable trajectories are generated. A control program was written for the Edison to obtain measurements, receive flight pattern commands, perform state estimation, calculate control laws, send motor speed commands to the Autopilot board, and log values. The program was written as a multithreaded C++ program for increased performance. A feedback linearization of the quadrotor\u27s dynamics was performed to account for its nonlinearities. A controller structure designed to ensure exponential Lyapunov stability was applied to the input-output linearized dynamics. The simplex method was used to aid the controller in pushing the Hummingbird\u27s actuators for aggressive maneuvers within set input limitations. The Edison\u27s Wi-Fi capabilities enable it to contact the Vicon server directly for position and orientation measurements. Accelerations and angular velocities are measured by the Autopilot\u27s inertial measurement unit (IMU). A quick state estimation process was implemented to filter the measured states, and state prediction was used to compensate for latency in the system. A custom circuit board and communication framework was designed and assembled for interfacing the Edison with the Autopilot. The custom communication framework allowed for a 16 times speed improvement over the default settings while bypassing the stock wireless communication\u27s inherently unreliable timing. The Hummingbird\u27s physical properties, such as propeller performance and rotational inertias, were characterized via static and step response experiments. The control system\u27s flight performance was evaluated through simulation and experimental tests

Advanced control designs for output tracking of hydrostatic transmissions

The work addresses simple but efficient model descriptions in a combination with advanced control and estimation approaches to achieve an accurate tracking of the desired trajectories. The proposed control designs are capable of fully exploiting the wide operation range of HSTs within the system configuration limits. A new trajectory planning scheme for the output tracking that uses both the primary and secondary control inputs was developed. Simple models or even purely data-driven models are envisaged and deployed to develop several advanced control approaches for HST systems

Brachiating power line inspection robot: controller design and implementation

The prevalence of electrical transmission networks has led to an increase in productivity and prosperity. In 2014, estimates showed that the global electric power transmission network consisted of 5.5 million circuit kilometres (Ckm) of high-voltage transmission lines with a combined capacity of 17 million mega-volt ampere. The vastness of the global transmission grid presents a significant problem for infrastructure maintenance. The high maintenance costs, coupled with challenging terrain, provide an opportunity for autonomous inspection robots. The Brachiating Power Line Inspection Robot (BPLIR) with wheels [73] is a transmission line inspection robot. The BPLIR is the focus of this research and this dissertation tackles the problem of state estimation, adaptive trajectory generation and robust control for the BPLIR. A kinematics-based Kalman Filter state estimator was designed and implemented to determine the full system state. Instrumentation used for measurement consisted of 2 Inertial Measurement Units (IMUs). The advantages of utilising IMUs is that they are less susceptible to drift, have no moving parts and are not prone to misalignment errors. The use of IMU's in the design meant that absolute angles (link angles measured with respect to earth) could be estimated, enabling the BPLIR to navigate inclined slopes. Quantitative Feedback Control theory was employed to address the issue of parameter uncertainty during operation. The operating environment of the BPLIR requires it to be robust to environmental factors such as wind disturbance and uncertainty in joint friction over time. The resulting robust control system was able to compensate for uncertain system parameters and reject disturbances in simulation. An online trajectory generator (OTG), inspired by Raibert-style reverse-time symmetry[10], fed into the control system to drive the end effector to the power line by employing brachiation. The OTG produced two trajectories; one of which was reverse time symmetrical and; another which minimised the perpendicular distance between the end gripper and the power line. Linear interpolation between the two trajectories ensured a smooth bump-less trajectory for the BPLIR to follow

Dynamic Bat-Control of a Redundant Ball Playing Robot

This thesis shows a control algorithm for coping with a ball batting task for an entertainment robot. The robot is a three jointed robot with a redundant degree of freedom and its name is Doggy . Doggy because of its dog-like costume. Design, mechanics and electronics were developed by us. DC-motors control the tooth belt driven joints, resulting in elasticities between the motor and link. Redundancy and elasticity have to be taken into account by our developed controller and are demanding control tasks. In this thesis we show the structure of the ball playing robot and how this structure can be described as a model. We distinguish two models: One model that includes a flexible bearing, the other does not. Both models are calibrated using the toolkit Sparse Least Squares on Manifolds (SLOM) - i.e. the parameters for the model are determined. Both calibrated models are compared to measurements of the real system. The model with the flexible bearing is used to implement a state estimator - based on a Kalman filter - on a microcontroller. This ensures real time estimation of the robot states. The estimated states are also compared with the measurements and are assessed. The estimated states represent the measurements well. In the core of this work we develop a Task Level Optimal Controller (TLOC), a model-predictive optimal controller based on the principles of a Linear Quadratic Regulator (LQR). We aim to play a ball back to an opponent precisely. We show how this task of playing a ball at a desired time with a desired velocity at a desired position can be embedded into the LQR principle. We use cost functions for the task description. In simulations, we show the functionality of the control concept, which consists of a linear part (on a microcontroller) and a nonlinear part (PC software). The linear part uses feedback gains which are calculated by the nonlinear part. The concept of the ball batting controller with precalculated feedback gains is evaluated on the robot. This shows successful batting motions. The entertainment aspect has been tested on the Open Campus Day at the University of Bremen and is summarized here shortly. Likewise, a jointly developed audience interaction by recognition of distinctive sounds is summarized herein. In this thesis we answer the question, if it is possible to define a rebound task for our robot within a controller and show the necessary steps for this

Adaptive Model Predictive Control for Engine-Driven Ducted Fan Lift Systems using an Associated Linear Parameter Varying Model

Ducted fan lift systems (DFLSs) powered by two-stroke aviation piston engines present a challenging control problem due to their complex multivariable dynamics. Current controllers for these systems typically rely on proportional-integral algorithms combined with data tables, which rely on accurate models and are not adaptive to handle time-varying dynamics or system uncertainties. This paper proposes a novel adaptive model predictive control (AMPC) strategy with an associated linear parameter varying (LPV) model for controlling the engine-driven DFLS. This LPV model is derived from a global network model, which is trained off-line with data obtained from a general mean value engine model for two-stroke aviation engines. Different network models, including multi-layer perceptron, Elman, and radial basis function (RBF), are evaluated and compared in this study. The results demonstrate that the RBF model exhibits higher prediction accuracy and robustness in the DFLS application. Based on the trained RBF model, the proposed AMPC approach constructs an associated network that directly outputs the LPV model parameters as an adaptive, robust, and efficient prediction model. The efficiency of the proposed approach is demonstrated through numerical simulations of a vertical take-off thrust preparation process for the DFLS. The simulation results indicate that the proposed AMPC method can effectively control the DFLS thrust with a relative error below 3.5%

Implementation and Control of an Inverted Pendulum on a Cart

An Inverted Pendulum on a Cart is a common system often used as a benchmark problem for control systems. The system consists of a cart that can move in one direction on the horizontal plane and a pendulum attached to the cart through a hinge point. The pendulum can rotate 360° on the plane made up of the vertical direction and the direction the cart can move. The system is controlled by applying a force to the cart, to make it move. This thesis consists of two goals. The first goal is to build a lab model of the Inverted Pendulum on a Cart system. The second goal is to create a controller that can swing the pendulum from a pendulum down position to a pendulum up position, and balance it in this position. The lab model is built using a track that the cart can move along, a stepper motor for applying force to the cart and a microcontroller for controlling the system. The pendulum angle and the cart position are measured using incremental encoders. A Mathematical model of the system have been derived. This forms the basis for the design of the controller and is also used for simulating and testing the system and controller in MATLAB/Simulink before it is implemented on the real system. The controller consists of three parts. An extended Kalman filter is implemented to estimate the non-measurable state. An energy-based controller is used to swing the pendulum from the down position to the up position. This controller regulates the energy in the pendulum to be close to the energy the pendulum should have when it is balanced in the upright position. When the pendulum is close to the upright position the controller will switch to a linear quadratic regulator to balance the pendulum. This controller is based on a linearized version of the mathematical system model. The lab model and the controllers have been successfully built and implemented

Control Theory in Engineering

The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation