# 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.