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Sampling-based motion planning works well in many cases but is less effective if the configuration space has narrow passages. In this paper, we propose a learning-based strategy to sample in these narrow passages, which improves overall planning time. Our algorithm first learns from the configuration space planning graphs and then uses the learned information to effectively generate narrow passage samples. We perform experiments in various 6D and 7D scenes. The algorithm offers one order of magnitude speed-up compared to baseline planners in some of these scenes. 

Using robots to collect data is an effective way to obtain information from the environment and communicate it to a static base station. Furthermore, robots have the capability to communicate with one another, potentially decreasing the time for data to reach the base station. We present a Mixed Integer Linear Program that reasons about discrete routing choices, continuous robot paths, and their effect on the latency of the data collection task. We analyze our formulation, discuss optimization challenges inherent to the data collection problem, and propose a factored formulation that finds optimal answers more efficiently. Our work is able to find paths that reduce latency by up to 101% compared to treating all robots independently in our tested scenarios. 

We present a learning-based approach to prove infeasibility of kinematic motion planning problems. Sampling-based motion planners are effective in high-dimensional spaces but are only probabilistically complete. Consequently, these planners cannot provide a definite answer if no plan exists, which is important for high-level scenarios, such as task-motion planning. We apply data generated during multi-directional sampling-based planning (such as PRM) to a machine learning approach to construct an infeasibility proof. An infeasibility proof is a closed manifold in the obstacle region of the configuration space that separates the start and goal into disconnected components of the free configuration space. We train the manifold using common machine learning techniques and then triangulate the manifold into a polytope to prove containment in the obstacle region. Under assumptions about the hyper-parameters and robustness of configuration space optimization, the output is either an infeasibility proof or a motion plan in the limit. We demonstrate proof construction for up to 4-DOF configuration spaces. A large part of the algorithm is parallelizable, which offers potential to address higher dimensional configuration spaces.

 

We present a learning-based approach to prove infeasibility of kinematic motion planning problems. Sampling-based motion planners are effective in high-dimensional spaces but are only probabilistically complete. Consequently, these planners cannot provide a definite answer if no plan exists, which is important for high-level scenarios, such as task-motion planning. We propose a combination of bidirectional sampling-based planning (such as RRT-connect) and machine learning to construct an infeasibility proof alongside the two search trees. An infeasibility proof is a closed manifold in the obstacle region of the configuration space that separates the start and goal into disconnected components of the free configuration space. We train the manifold using common machine learning techniques and then triangulate the manifold into a polytope to prove containment in the obstacle region. Under assumptions about learning hyper-parameters and robustness of configuration space optimization, the output is either an infeasibility proof or a motion plan. We demonstrate proof construction for 3-DOF and 4-DOF manipulators and show improvement over a previous algorithm. 

Task and motion planning operates in a combined discrete and continuous space to find a sequence of high-level, discrete actions and corresponding low-level, continuous paths to go from an initial state to a goal state. 

Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.