Motion planning for closed-chain systems is particularly difficult due to additional closure constraints placed on the system. In fact, the probability of randomly selecting a set of joint angles that satisfy the closure constraints is zero. We propose planning with reachable distance (PRD) to overcome this challenge by first precomputing the subspace satisfying the closure constraints, then directly sampling in it. To do so, we represent the chain as a hierarchy of sub-chains. Then we calculate the "closure" sub-space as appropriate reachable distance ranges of sub-chains satisfying the closure constraints. This provides two distinct advantages over traditional approaches: (1) configurations are quickly sampled and converted to joint angles using basic trigonometry functions instead of more expensive inverse kinematics solvers, and (2) configurations are guaranteed to be closed. In this paper, we describe this hierarchical chain representation and give a sampling algorithm with complexity linear in the number of links. We provide the necessary motion planning primitives for most sampling-based motion planners. Our experimental results show our method is fast, making sampling closed configurations comparable to sampling open chain configurations that ignore closure constraints. Our method is general, easy to implement, and also extends to other distance-related constraints besides the ones demonstrated here

With the success of randomized sampling-based motion planners such as probabilistic roadmap methods, much work has been done to design new sampling techniques and distributions. To date, there is no sampling technique that outperforms all other techniques for all motion planning problems. Instead, each proposed technique has different strengths and weaknesses. However, little work has been done to combine these techniques to create new distributions. In this paper, we propose to bias one sampling distribution with another such that the resulting distribution out-performs either of its parent distributions. We present a general framework for biasing samplers that is easily extendable to new distributions and can handle an arbitrary number of parent distributions by chaining them together. Our experimental results show that by combining distributions, we can out-perform existing planners. Our results also indicate that not one single distribution combination performs the best in all problems, and we identify which perform better for the specific application domains studied

Tree-based path planners have been shown to be well suited to solve various high dimensional motion planning problems. Here we present a variant of the Rapidly-Exploring Random Tree (RRT) path planning algorithm that is able to explore narrow passages or difficult areas more effectively. We show that both workspace obstacle information and C-space information can be used when deciding which direction to grow. The method includes many ways to grow the tree, some taking into account the obstacles in the environment. This planner works best in difficult areas when planning for free flying rigid or articulated robots. Indeed, whereas the standard RRT can face difficulties planning in a narrow passage, the tree based planner presented here works best in these areas

We propose a novel, motion planning based approach to approximately map the energy landscape of an RNA molecule. Our method is based on the successful probabilistic roadmap motion planners that we have previously successfully applied to protein folding. The key advantage of our method is that it provides a sparse map that captures the main features of the landscape and which can be analyzed to compute folding kinetics. In this paper, we provide evidence that this approach is also well suited to RNA. We compute population kinetics and transition rates on our roadmaps using the master equation for a few moderately sized RNA and show that our results compare favorably with results of other existing methods.