Algebraic approach to model and plan robotic manipulation tasks

 Task planning is becoming increasingly important with the development of more complex and capable robotic systems. Traditionally, the goal of performing plans is to determine the correct sequence of actions that will lead to a desired state. For our tasks, we established manipulation elements with geometric, kinematic, and contact information. By using dual-quaternion algebra it is possible to compactly and consistently express those components.

Then, by defining states and composition operations, we are able to model high-level manipulation tasks. In addition, by taking advantage of the physical structure of the problem and the expressiveness of dual quaternions, we are developing an algebraic approach that will lead us to model manipulation tasks, express their dynamical behavior, and execute synthesized plans using robotic systems.

Whole-body modeling and control for humanoid robots

  The research on humanoid robots has been increasing in the last years. One of the reasons is that to interact with humans and to handle objects made by and for human beings, robots should have an anthropomorphic structure. In this context, humanoids can be used to assist humans or even to perform tasks that a person would do. Indeed, humanoid robots have a great number of relevant applications as, for example, in hazardous or inhabited environments exploration, military purposes, assistance of elderly and disabled people and delivery of packages and documents in offices.

 Bipedal humanoid robots walk by the gait, which must be controlled to guarantee a balanced motion. Besides that, it is important to develop control strategies allowing the robot to perform multiple tasks as best as possible. Two approaches are used in this project: the decoupled control and the whole-body control. The decoupled control treats the legs and the upper body as separate parts. This approach focuses on gait control, allowing the robot to walk and perform some tasks in the upper body, simultaneously, keeping the robot balanced. A whole-body control can be used to achieve a better functionality using all degrees of freedom available and making movements smoother. Using dual quaternion algebra, a kinematic whole-body control can be developed to execute a large number of simultaneous tasks for a humanoid robot.

Cooperative manipulation using a consensus-based approach

Some robotic applications can be improved when replacing a single and complex system by another consisting of several simple agents, forming a distributed and cooperative multi-agent system. An approach in control theory which enables this type of system to work cooperatively is called consensus problem, whose goal is to make the agents reach an agreement on the value of a particular variable of interest. This approach allows us to represent some problems in robotics, like formation control, swarms, leader-follower, rendezvous, etc., using simple control laws---the consensus protocols---based on the exchange of information among the agents. In this line of research we apply consensus theory to the problem of cooperative manipulation between mobile manipulators. In this case, for example, the goal can be to make the end-effectors of all agents achieve the same configuration with respect to the object being manipulated. Another example would be making a formation around the object before grasping it.

Convertible UAVs for search-and-rescue missions and load transportation

Convertible Unmanned Aerial Vehicles (UAVs) combine the advantages of airplanes and rotorcrafts as improved forward speed, hovering, vertical take-off and landing (VTOL) capabilities. Such vehicles become suitable for search-and-rescue missions and load transportation, due to the necessity of rapid deployment in risk zones, such as ones affected by natural, nuclear or chemical disasters, which is a task mostly unfeasible for larger vehicles.

Since a Tilt-rotor UAV usually changes between helicopter and airplane operation modes by tilting its rotors, the enlarged flight envelope imposes challenges to control design. In forward flight, by making use of aerodynamic surfaces the longitudinal and lateral-directional motions are controlled. However, in helicopter-flight mode, such aerodynamic surfaces do not produce significant effects, being the controllability achieved by means of its rotors. Using a multi-body dynamic modeling and a wide aerodynamic characterization, a full flight envelope mathematical model of the Tilt-rotor UAV can be obtained for computer simulations and designing of several control techniques, including MPC, and robust adaptive controllers based on a mixing polytopic approach for smooth full flight envelope trajectory tracking.

On the other hand, for transportation tasks the suspended load is usually connected to the convertible UAV by means of a rope, considerably changing its dynamic behavior and further adding unactuated degrees of freedom to the mechanical system. Among the resulting difficulties, if the load swing is not properly attenuated, the whole system can become unstable, leading to mission failure. Moreover, precise positioning of the load requires the knowledge of the load pose with respect to an inertial frame, which is usually not directly measured by available sensors located at the aircraft. To cope with the resulting difficulties, robust control strategies can be designed based on whole-body dynamic equations, either for the load swing attenuation problem or for path tracking of the load, and state estimators can be developed to provide information on the position of the load, based on stochastic or set-membership techniques.

Fault-tolerant control based on set-theoretic methods

Requirements on reliability and safety of control systems under actuator and sensor malfunctions motivated the development of Fault-tolerant Control (FTC) and Fault Detection and Isolation (FDI) strategies since the 70’s. The purpose of such strategies is to accommodate component failures by maintaining the overall system stable with acceptable closed-loop performance in faulty scenarios, changing control objectives if necessary to cope with physical limitations imposed by the faults. In particular, these control strategies have been of utmost importance in safety critical systems, such as nuclear power plants and aerospace systems, in which minor faults in components may lead to catastrophic consequences if not treated properly. In UAV applications, the occurrence of faults in components such sensor and actuators, or even in the controllers or the UAV communication channels, are capable of leading to mission failure with potential damage to the unmanned aerial system.

FTC and FDI strategies based on set-theoretic methods are promising and distinguished approaches being developed recently. These methods are based on computation with sets, either under set-theoretic concepts such as positive invariance, set-membership methodology or through numerical tools such as interval arithmetic. They are characterized by their robustness and reliability, since the obtained results are usually guaranteed in a formal manner. A common set-theoretic approach is the use of set-valued state estimators to perform reliable fault detection and isolation, which can be based, for instance, on interval arithmetic, convex polytopes, ellipsoids, zonotopes, or constrained zonotopes.