Motion and Manipulation Planning with User Guidance

Robot motion is controlled in the joint space whereas the robots have to perform tasks in their task space. Many tasks like carrying a glass of liquid, pouring liquid, opening a drawer, manipulating a heavy object by pivoting, requires constraints on the end-effector during the motion. The forward and inverse position kinematic mappings between joint space and task space are highly nonlinear and multi-valued (for IK). Consequently, modeling task space constraints like keeping the orientation of the end-effector fixed while changing its position (which is required for carrying a cup of liquid without spilling) is quite complex in the joint space. In this work, we show that the use of Screw Linear Interpolation (ScLERP) to plan motions in the task space combined with resolved motion rate control to compute the corresponding joint space path, allows one to satisfy many common task space motion constraints in motion planning, without explicitly modeling them. In particular, any motion constraint that forms a one-parameter subgroup of the group of rigid body motions can be incorporated in our planning scheme, without explicit modeling. We further extend this motion planning scheme to a local motion planner that can satisfy collision avoidance constraints. The collision avoidance is done with a novel kinematic state evolution model of the robot where the collision avoidance is encoded as a complementarity constraint. We show that the kinematic state evolution with collision avoidance can be represented as a Linear Complementarity Problem (LCP). Using the LCP model along with screw linear interpolation, we show that it may be possible to compute a path between two given task space poses by directly moving from the current pose to the goal pose, even if there are potential collisions with obstacles. The local planner can be incorporated into any sampling-based global motion planning scheme.

We develop a real-time point-to-point kinematic task-space planner based on screw interpolation that implicitly follows the underlying geometric constraints from a user demonstration. We demonstrate through example scenarios that implicit task constraints in a single user demonstration can be captured in our approach. One key feature of the proposed planner is that it does not learn a trajectory or intend to imitate a human trajectory, but rather explores the geometric features in the demonstration throughout a one-time guidance and extend such features as constraints in a generalized path generator. In this sense, the framework allows for generalization of initial and final configurations, it accommodates path disturbances, and it is agnostic to the robot being used. We evaluate our approach on the 7 DOF Baxter robot on a multitude of common tasks and also show generalization ability of our method with respect to different conditions.