Aykut C. Satici

Robust Optimal Control of Quadrotor UAVs

This paper provides the design and implementation of an L1-optimal control of a quadrotor unmanned aerial vehicle (UAV). The quadrotor UAV is an underactuated rigid body with four propellers that generate forces along the rotor axes. These four forces are used to achieve asymptotic tracking of four outputs, namely the position of the center of mass of the UAV and the heading. With perfect knowledge of plant parameters and no measurement noise, the magnitudes of the errors are shown to exponentially converge to zero. In the case of parametric uncertainty and measurement noise, the controller yields an exponential decrease of the magnitude of the errors in an L1-optimal sense. In other words, the controller is designed so that it minimizes the L∞-gain of the plant with respect to disturbances. The performance of the controller is evaluated in experiments and compared with that of a related robust nonlinear controller in the literature. The experimental data shows that the proposed controller rejects persistent disturbances, which is quantified by a very small magnitude of the mean error.

Tracking Control of Mobile Robots Localized via Chained Fusion of Discrete and Continuous Epipolar Geometry, IMU and Odometry

This paper presents a novel navigation and control system for autonomous mobile robots that includes path planning, localization, and control. A unique vision-based pose and velocity estimation scheme utilizing both the continuous and discrete forms of the Euclidean homography matrix is fused with inertial and optical encoder measurements to estimate the pose, orientation, and velocity of the robot and ensure accurate localization and control signals. A depth estimation system is integrated in order to overcome the loss of scale inherent in vision-based estimation. A path following control system is introduced that is capable of guiding the robot along a designated curve. Stability analysis is provided for the control system and experimental results are presented that prove the combined localization and control system performs with high accuracy.

Connectivity preserving formation control with collision avoidance for nonholonomic wheeled mobile robots

The preservation of connectivity in mobile robot networks is critical to the success of existing algorithms designed to achieve various goals. The available connectivity control algorithms mainly work through preservation of existing edges in the network. A link may be deleted if distributed decision making determines that the edge is not a cut-bridge. A controller is presented which allows edges to be broken in a continuous manner without higher-level decision making. The controller is based on maximization of the second smallest eigenvalue of the graph Laplacian. The controllers are designed for holonomic robots, and are extended for implementation on non-holonomic wheeled mobile robots. Finally, the performance of the extended controllers are demonstrated experimentally.

Leader-follower formation control of nonholonomic wheeled mobile robots using only position measurements

This paper deals with the formation control problem for a team of nonholonomic wheeled mobile robots. Each robot has a leader robot with respect to which a constant relative position is to be maintained, except for a single robot which defines the motion of the formation. We present a feedback control method that guarantees convergence of the relative position of any follower robot (with respect to its leader) to desired values. The controller does not require sensing of the leaders velocity. Instead, an adaptive method is used to estimate the leaders forward velocity. The resulting closed loop system is shown to be semi-globally asymptotically stable. Simulation results are presented in order to demonstrate the performance of the controller for two robots, and a team of mobile robots.

Formation control of wheeled robots with vision-based position measurement

Many applications require multiple mobile robots to move with a common velocity and at fixed relative distances. We present a time-invariant, state-feedback control law and a novel vision-based pose reconstruction system that allows one differential drive robot to follow another at a constant relative distance. The control law does not require measurement or estimation of the leader robot velocity and has tunable parameters that allows one to prioritize the error bounds of the desired states. The proposed pose reconstruction algorithm is computationally inexpensive and reliable. We present experimental results on two iRobot Create robots showing the performance of the controller and vision algorithm.

An Optimal Trajectory Planner for a Robotic Batting Task: The Table Tennis Example

This paper presents an optimal trajectory planner for a robotic batting task . The specific case of a table tennis game performed by a robot is considered. Given an estimation of the trajectory of the ball during the free flight, the method addresses the determination of the paddle configuration (pose and velocity) to return the ball at a desired position with a desired spin. The implemented algorithm takes into account the hybrid dynamic model of the ball in free flight as well as the state transition at the impact (the reset map). An optimal trajectory that minimizes the acceleration functional is generated for the paddle to reach the desired impact position, velocity and orientation. Simulations of different case studies further bolster the approach along with a comparison with state-of-the-art methods.

Path-following control for mobile robots localized via sensor-fused visual homography

This paper presents a novel navigation and control system for wheeled mobile robots that includes path planning, localization, and control. A path following control system is introduced that is capable of guiding and keeping the robot on a designated curve. Localization and velocity estimation are provided by a unique sensor fusion algorithm that incorporates vision, IMU and wheel encoder data. Stability analysis is provided for the control system, and experimental results are presented that prove the combined localization and control system performs with high accuracy.

Nonholonomic cooperative manipulation of polygonal objects in the plane

This paper presents a framework in which a group of nonholonomic wheeled robot manipulators are cooperatively utilized to manipulate a polygonal object in SE(2). In this framework, the robots are assumed to contact the object without friction, applying forces only in the normal direction. The dynamics of the whole system can be decomposed into task and nullspaces (internal motions). The desired object pose is achieved by controlling the task-space. On the other hand, as the contact point is driven to its desired value by controlling the internal motions, force-closure is ensured. An extensive simulation study is presented to validate the proposed framework.

Intrinsic dynamics and total energy-shaping control of the ballbot system

ABSTRACT Research on bipedal locomotion has shown that a dynamic walking gait is energetically more efficient than a statically stable one. Analogously, even though statically stable multi-wheeled robots are easier to control, they are energetically less efficient and have low accelerations to avoid tipping over. In contrast, the ballbot is an underactuated, nonholonomically constrained mobile robot, whose upward equilibrium point has to be stabilised by active control. In this work, we derive coordinate-invariant, reduced, Euler–Poincaré equations of motion for the ballbot. By means of partial feedback linearisation, we obtain two independent passive outputs with corresponding storage functions and utilise these to come up with energy-shaping control laws which move the system along the trajectories of a new Lagrangian system whose desired equilibrium point is asymptotically stable by construction. The basin of attraction of this controller is shown to be almost global under certain conditions on the design of the mechanism which are reflected directly in the mass matrix of the unforced equations of motion.

A coordinate-free framework for robotic pizza tossing and catching

In this work, we demonstrate how autonomous pizza tossing and catching can be achieved. Under the assumption that the pizza dough is grasped by a number of fingers with soft contact, we formulate the grasp constraints and use them to derive the individual and combined Euler-Lagrange dynamic equations of motion of the robotic manipulator and the dough. In particular, the dynamics of the dough is a modified version of the rigid-body dynamics, taking into account the change of inertia due to its deformation. Armed with these mathematical models, we tackle the two control problems of tossing and catching. For the tossing phase, we derive an exponentially convergent controller that stabilizes a desired velocity of the dough as it is let go. On the other hand, so as to catch the dough, we generate an optimal trajectory for the end-effector of the robotic manipulator. Finally, we derive control laws to make the optimal trajectory exponentially attractive. We demonstrate the developed theory with an elaborate simulation of the tossing and catching phases.