text: Before beginning any robot task, users must position the robot's base, a task that now depends entirely on user intuition. While slight perturbation is tolerable for robots with moveable bases, correcting the problem is imperative for fixed-base robots if some essential task sections are out of reach. For mobile manipulation robots, it is necessary to decide on a specific base position before beginning manipulation tasks. This paper presents Reuleaux, an open source library for robot reachability analyses and base placement. It reduces the amount of extra repositioning and removes the manual work of identifying potential base locations. Based on the reachability map, base placement locations of a whole robot or only the arm can be efficiently determined. This can be applied to both statically mounted robots, where position of the robot and work piece ensure the maximum amount of work performed, and to mobile robots, where the maximum amount of workable area can be reached. Solutions are not limited only to vertically constrained placement, since complicated robotics tasks require the base to be placed at unique poses based on task demand. All Reuleaux library methods were tested on different robots of different specifications and evaluated for tasks in simulation and real world environment. Evaluation results indicate that Reuleaux had significantly improved performance than prior existing methods in terms of time-efficiency and range of applicability.
  @cite_0: 
  @cite_1: Mobile humanoid robots have the capability of accomplishing complex tasks in human dominated environments. In order to execute a task with its arm, a robot needs to place its base reasonably first. In previous work, a positionbased reachability map solved this problem by matching a precomputed inverse kinematics database with discretized versions of the task path. However, its capability is restricted to the end effector with which the database was computed. This paper proposes an orientation-based reachability map which supports on-line end effector frame extensions. The added extension capability enables robots to handle partially constrained task paths with different tool frames, which would be non-trivial for previous methods without recomputing a reachability map. We discuss the differences between the new method and its predecessors, and analyze extension transformation matrix to provide mathematical proof for the extension capability of our reachability map. Our experimental results show that the orientation-based reachability map is as fast as the positionbased reachability map while benefiting from the additional extension capability.
  @cite_3: Humanoid robots are envisioned in general household tasks. To be able to fulfill a given task the robot needs to be equipped with knowledge concerning the manipulation and interaction in the environment and with knowledge about its own capabilities. When performing actions, e.g. opening doors or imitating human reach to grasp movements special 3-d trajectories are followed with the robot's end-effector. These trajectories can not be executed in every part of the robot's arm workspace. Therefore a task planner has to determine if and how additional degrees of freedom such as the robot's upper body or the robot's base can be moved in order to execute the task-specific trajectory. An approach is presented that computes placements for a mobile manipulator online given a task-related 3-d trajectory. A discrete representation of the robot arm's reachable workspace is used. Task-specific trajectories are interpreted as patterns and searched in the reachability model using multi-dimensional correlation. The relevance of the presented approach is demonstrated in simulated positioning tasks.
  @cite_2: For mobile manipulators envisioned in home environments a kitchen scenario provides a challenging testbed for numerous skills. Diverse manipulation actions are required, e.g. simple pick and place for moving objects and constrained motions for opening doors and drawers. The robot kinematics and link limits however are restrictive. Therefore especially a constrained trajectory will not be executable from arbitrary placements of the mobile manipulator. A two stage approach is presented to position a mobile manipulator to execute constrained linear trajectories as needed for opening drawers. In a first stage, a representation of a robot armpsilas reachable workspace is computed. Pattern recognition techniques are used to find regions in the workspace representation where these trajectories are possible. A set of trajectories results. In the second stage mobile manipulator placements are computed and the corresponding trajectories are checked for collisions. Compared to a brute force search through the workspace, the success rate of finding a mobile manipulator placement can be increased from 2 to 70 .
summary: To overcome the single grasp location issue, several papers extended the inverse reachability problem to solve for trajectories. Various methods have been used to search the reachability map in order to find the location where the desired trajectory can be executed with the highest level of dexterity. @cite_0 uses sampling of the trajectory to find and overlay multiple base placements; @cite_2 uses a pattern search to fit the trajectory into the area representing the field of high dexterity; and @cite_3 uses a cross-correlation technique to fit the desired trajectory to the model of the robot reachability map. Further improvements to the reachability map method were developed by @cite_1 to include the ability to add a transform offset from the original end-effector location, which is useful if the robot is grasping a tool with a non-zero length.