An apparatus and a method for planning contact-interaction trajectories are provided. The apparatus is a robot that accepts contact interactions between the robot and the environment. The robot stores a dynamic model representing geometric, dynamic, and frictional properties of the robot and the environment, and a relaxed contact model to representing dynamic interactions between the robot and the object via virtual forces. The robot further determines, iteratively until a termination condition is met, a trajectory, associated control commands for controlling the robot, and virtual stiffness values by performing optimization reducing stiffness of the virtual force and minimizing a difference between the target pose of the object and a final pose of the object moved from the initial pose. Further, an actuator moves a robot arm of the robot according to the trajectory and the associated control commands.

An apparatus and a method for planning contact-interaction trajectories are provided. The apparatus is a robot that accepts contact interactions between the robot and the environment. The robot stores a dynamic model representing geometric, dynamic, and frictional properties of the robot and the environment, and a relaxed contact model to representing dynamic interactions between the robot and the object via virtual forces. The robot further determines, iteratively until a termination condition is met, a trajectory, associated control commands for controlling the robot, and virtual stiffness values by performing optimization reducing stiffness of the virtual force and minimizing a difference between the target pose of the object and a final pose of the object moved from the initial pose. Further, an actuator moves a robot arm of the robot according to the trajectory and the associated control commands.