In these years one of the fields that is having the most rapid developments is the robotics. With robotics, today, we intend the design, construction, operation, and application of automated machines in human life. We can find robots mainly in industries, where they automate processes of work, but it is becoming increasingly important the market of social robots, that are robots built to stay closely to the human, interacting in our daily activities. These robots usually do a limit number of actions, and they are not provide good learning capacity.
However, the long great goal of robotics is developing new architectures that imitate real natural systems behaviour, and if it is possible, create a humanoid robot that act and think like us.
How the human brain accomplishes all the complex tasks that we do is not yet completely clear and for this reason is quite hard to build a robot similar to us. However, thanks to the use of new and smarter materials and to studies in mechanics,electronics, artificial intelligence and biology, barriers that seemed insurmountable a years ago now are not anymore; recent robots are more complex and efficient compared to the past and in a sense, they are able to reproduce some human behaviour, also if these are complex.
There are still several issues that have not yet been solved, and now new studies are searching new solutions keeping inspiration from nature, that is bio-inspired robotics. In particular, bio-inspired robotics aims at reproducing, among other things, the ability of humans in autonomous movements and development of learning capabilities in robot, allowing them to stay in a dynamic environment. Movements allow to interact with the world and at the same time a way to develop new goals and to satisfy them. Some movements are available from birth and they represent survival and exploratory functions, which enable humans to build sensorimotor maps that we use as the basis for other elements activities .
We need a biologically inspired model for the generation and adaptation of the movements. We want to make a contribution to finding a solution that would allow complex robots to move, that is a problem where classical control show their limit due to an high number of degree of freedom. The main concept is imitation learning. Different studies on biology have showed that this concept exist in human brain, where some areas are active through the observation of a behaviour  . Imitation learning evidences are not only in biology studies but also in psychology, where has been found imitative behaviour in newborn and animals  . These studies and many others bring out the importance of imitation in motor learning.
The way chosen to represents movements learned from imitation are the motor primitives. Also they are important in motor learning field and their theory has been discovered in biology. Many studies have been done about motor primitives studying brain signals  , showing that the creation of a movement is composed by simple patterns linked together. From here in robotics was born the idea to represent this basic block in a mathematical way, so that the generation of the movement is biologically similar to the human beings.
Many mathematical model have been developed to formalize motor primitives  , but probably the most bio-inspired is the Dynamic Movement Primitives (DMP) that provides a representation in terms of kinematic primitives; it has important properties to make it easy to learn the model. We will see how this model can be integrated in a humanoid robot and its application in tests that will lead us to observe a human-similar behaviour. In a first experiment, we have shown to the robot a movement primitives, the motion of pouring coffee into a glass. With DMP system it was created a kinematic representation of the movement through different parameters. In this way, changing initial positions of the movement the robot however has reached is target, the glass in this case, with a behaviour qualitatively similar to the taught one. The same is was valid also with the changing of goal position. In a second experiment we have exploited one of the property of DMP to allow the robot to avoid obstacles. Through adding a further term in the system, DMP are able to adapt themselves to changes of the environment. We have taught to the robot a reaching-like task and we have put on its movement trajectory an obstacle. Although the presence of one, or more, obstacles the robot is able to complete its task and to reach the goal with a modified trajectory.
The collected experimental results have demonstrated that this model is appropriate for motor learning, and also for reactive control. Several more tests are required to highlight better the limits of this representation; up to now has emerged that the proposed model lacks of a module to adapt movement not only based on the start and final position, but also to the quality of the entire trajectory. For example, if we would like to teach a robot to write a letter, we have to think a model that allows it to write the letter taught, with correct scale and characteristics,from any starting point.
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