Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

An Interior Point Method Solving Motion Planning Problems with Narrow Passages

Algorithmic solutions for the motion planning problem have been investigated for five decades. Since the development of A* in 1969 many approaches have been investigated, traditionally classified as either grid decomposition, potential fields or sampling-based. In this work, we focus on using numerical optimization, which is understudied for solving motion planning problems. This lack of interest in the favor of sampling-based methods is largely due to the non-convexity introduced by narrow passages. We address this shortcoming by grounding the solution in differential geometry. We demonstrate through a series of experiments on 3 Dofs and 6 Dofs narrow passage problems, how modeling explicitly the underlying Riemannian manifold leads to an efficient interior-point non-linear programming solution.Comment: IEEE RO-MAN 2020, 6 page

Goal Set Inverse Optimal Control and Iterative Re-planning for Predicting Human Reaching Motions in Shared Workspaces

To enable safe and efficient human-robot collaboration in shared workspaces it is important for the robot to predict how a human will move when performing a task. While predicting human motion for tasks not known a priori is very challenging, we argue that single-arm reaching motions for known tasks in collaborative settings (which are especially relevant for manufacturing) are indeed predictable. Two hypotheses underlie our approach for predicting such motions: First, that the trajectory the human performs is optimal with respect to an unknown cost function, and second, that human adaptation to their partner's motion can be captured well through iterative re-planning with the above cost function. The key to our approach is thus to learn a cost function which "explains" the motion of the human. To do this, we gather example trajectories from pairs of participants performing a collaborative assembly task using motion capture. We then use Inverse Optimal Control to learn a cost function from these trajectories. Finally, we predict reaching motions from the human's current configuration to a task-space goal region by iteratively re-planning a trajectory using the learned cost function. Our planning algorithm is based on the trajectory optimizer STOMP, it plans for a 23 DoF human kinematic model and accounts for the presence of a moving collaborator and obstacles in the environment. Our results suggest that in most cases, our method outperforms baseline methods when predicting motions. We also show that our method outperforms baselines for predicting human motion when a human and a robot share the workspace.Comment: 12 pages, Accepted for publication IEEE Transaction on Robotics 201

Neural Networks in Mobile Robot Motion

This paper deals with a path planning and intelligent control of an autonomous robot which should move safely in partially structured environment. This environment may involve any number of obstacles of arbitrary shape and size; some of them are allowed to move. We describe our approach to solving the motion-planning problem in mobile robot control using neural networks-based technique. Our method of the construction of a collision-free path for moving robot among obstacles is based on two neural networks. The first neural network is used to determine the "free" space using ultrasound range finder data. The second neural network "finds" a safe direction for the next robot section of the path in the workspace while avoiding the nearest obstacles. Simulation examples of generated path with proposed techniques will be presented.Comment: 9 Page