Task space constraints invariably arise in the practical operation of robotic systems, both in service and industrial applications; examples include opening a door, transporting an object, cooperating with other robots, executing a given end-effector trajectory for drawing, cutting or welding, tracking a visual target. Redundant robotic systems, such as humanoids and mobile manipulators, posses the dexterity for accomplishing these tasks while pursuing additional objectives, among which the most important is obstacle avoidance. A motion planner should be able to generate robot motions that satisfy the task space constraints while guaranteeing that the robot body does not collide with workspace obstacles or with parts of itself (self-collision). This problem is referred to as Task-Constrained Motion Planning (TCMP).
Previous approaches to the solution (see, e.g., 1, 2) are based on the idea of sampling and inverting the task constraint to build a roadmap of task-constrained configurations which are then connected by simple local paths; hence, task tracking is not enforced during the motion between samples. To overcome this problem, we have developed a control-based approach based on a motion generation scheme that guarantees continued satisfaction of such constraint. The resulting randomized planner allows to achieve accurate execution of the desired task without increasing the complexity of the roadmap.
 G. Oriolo, M. Vendittelli, A control-based approach to task-constrained motion planning, 2009 IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, St. Louis, USA, Oct. 2009, pp. 297-302. (download)
Here we present preliminary results obtained for a fixed-base manipulator, a noholonomic mobile manipulator and a free-fying mobile manipulator.
The first two
experiments have been performed on the DLR Light Weight Robot, a
dextrous manipulator with 7 revolute joints. The task is to follow an
assigned path for the position of the end-effector. In both the
experiments, the last three degrees of freedom (the wrist) are blocked;
the degree of redundancy is therefore equal to 1. To better evaluate
the practical improvement introduced by the proposed strategy, we have
solved two planning problems of increasing difficulty. The values of
both the mean and the maximum tracking error obtained with the
randomized control-based approach are smaller by almost two orders of
magnitude than those obtained by using an RRT planning strategy with a
linear local planner. This improvement in accuracy is obtained without
an increase in the complexity (number of nodes) of the roadmap.
Experiment 1: DLR Light Weight Robot (AVI clip). The given end-effector path is a straight segment, of length equal to 120 cm, passing through the window placed in front of the manipulator.
Experiment 2: DLR Light Weight Robot (AVI clip). The path and the window were moved further right w.r.t. the base of the manipulator. This generates a noarrow passage in the constrained configuration space (i.e., the set of configurations satisfying the task constraint) that complicates the search of a collision-free path satisfying the task constraint.
Experiment 3: A 3-dof manipulator on a wheeled base with the kinematics of the unicycle with a limited turning radius. The manipulator end-effector path is about 5 m long. In the first experiment (AVI clip) the solution path contains self-motions, while in the second (AVI clip) self-motion have not been allowed.
Experiment 4: A 4-dof robot on a 3-dof free-flying base (AVI clip). The robot has to follow a 33 m path with its end-point inside a pipe of variable radius.