Image-based trajectory robot programming planning approach

A system for executing at least one task learned by observation of at least one set of demonstrations, comprising:

• at least one robot with at least one movable end-effector;
• at least one object to be manipulated by the at least one end-effector;
• at least one fixed camera for observing said at least one set of demonstrations of the at least one task, resulting in at least one set of observed task trajectories, and observing the execution of said at least one task by said at least one robot;
• at least one processing unit for generating a generalized task trajectory from said at least one set of observed task trajectories;
• at least one controller for servoing said at least one robot to reproduce the task with its end-effector in the field of view of said at least one said fixed camera using image-based visual servoing to minimize the difference between the observed trajectory during the execution and the generalized task trajectory,
• whereas a reference task trajectory is obtained by performing a smoothing of said set of observed task trajectories, and
• whereas said generalized task trajectory is obtained by performing a second order conic optimization of the reference task trajectory within a set of constraints imposed on said observed task trajectories and said at least one robot.