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Efficient Planning of Spatially Constrained Robot Using Reachable Distances

Motion planning for spatially constrained robots is particularly difficult due to additional constraints placed on the robot, such as closure constraints for closed chains or requirements on end effector placement for articulated linkages. In fact, for many spatially constrained systems, the probability that a randomly sampled robot configuration satisfies the additional constraints approaches zero. It is usually too computationally expensive to compute the portion of configuration space that lies on the constraint surface. We overcome this challenge by redefining the robot’s degrees of freedom into a new set of sampling parameters that enable us to sample the constraint surface directly. For example, articulated linkages are typically sampled by randomly selecting values for each joint angle. Instead, we redefine the articulated linkage and its additional constraints into reachable distance space. The unique property of reachable distance space is that all configurations in that space lie on the constraint surface. Thus, we sample in reachable distance space instead of configuration space to directly sample on the constraint surface. In previous work, we demonstrated that this reachable distance formulation is extremely efficient for sampling and planning closed chain systems. Here, we generalize our reachable distance framework to include other types of spatially constrained systems. We demonstrate its utility on a variety of spatially constrained systems including restricted end effector sampling for articulated linkages, on-line planning for drawing (or sculpting), and closed chain planning. In particular, we show that we can sample the constraint surface with complexity linear in the complexity of the robot system. Our method outperforms other randomized sampling methods such as prm and rrt for sampling and planning for these spatially constrained systems.