Maximizing Robot Manipulability along Paths in Collisionfree Motion Planning A major task in motion planning is to find suitable movements with large manipulability, while collisionfree operation must be guaranteed. This condition is increasingly important in the collaboration between humans and robots, as the capability of avoidance to humans or dynamic obstacles must be ensured anytime. For this purpose, paths in motion planning have to be optimized with respect to manipulability and distance to obstacles. Because with a large manipulability the robot has at any time, the possibility of evading due to the greater freedom of movement. Alternatively, the robot can be pushed away by using a Cartesian impedance control. To achieve this, we have developed a combined approach. First, we introduce a Rapidlyexploring Random Tree, which is extended and optimized by state costs for manipulability. Secondly, we perform an optimization using the STOMP method and Gaussian Mixture Models. With this dual approach we are able to find paths in narrow passages and simultaneously optimize the path in terms of manipulability.

Fast Manipulability Maximization Using ContinuousTime Trajectory optimization A significant challenge in manipulation motion planning is to ensure agility in the face of unpredictable changes during task execution. This requires the identification and possible modification of suitable jointspace trajectories, since the joint velocities required to achieve a specific endeffector motion vary with manipulator configuration. For a given manipulator configuration, the joint spacetotask space velocity mapping is characterized by a quantity known as the manipulability index. In contrast to previous controlbased approaches, we examine the maximization of manipulability during planning as a way of achieving adaptable and safe joint spacetotask space motion mappings in various scenarios. By representing the manipulator trajectory as a continuoustime Gaussian process (GP), we are able to leverage recent advances in trajectory optimization to maximize the manipulability index during trajectory generation. Moreover, the sparsity of our chosen representation reduces the typically large computational cost associated with maximizing manipulability when additional constraints exist. Results from simulation studies and experiments with a real manipulator demonstrate increases in manipulability, while maintaining smooth trajectories with more dexterous (and therefore more agile) arm configurations.