Interest in robot manipulators interacting with dynamic environments has been continuously growing because of the increasing demand for industrial robot collaboration. Human-robot collaboration and robot-robot collaboration are the two scenarios of robot collaboration that have generally been considered. The difficulties of such applications may be described from two perspectives: a good perception of environment and a proper algorithm to react to the dynamic environment for the robot manipulators. Online trajectory generation is one of the approaches for robot reaction. In the generation of the trajectory, the transformation between joint space and task space is necessary since the sensor measurement of the environment is in task space and the trajectory of the robot manipulator is in joint space. The transformation needs to be done online in a dynamic environment and hence easily results in an exponential increase of the computational load.;This dissertation proposes a safety index and the associated robot safety system in order to assess and ensure the safety of the agent in the collaboration scenarios. The agent could be a human worker in human-robot collaboration or another robot in robot-robot collaboration. In the robot safety system, the online trajectory generation algorithm is formulated in the optimization-based trajectory planning framework. The safety index is evaluated using the ellipsoid coordinates attached to the robot links that represents the distance between the robot manipulator and the agent. To account for the inertial effect, the momentum of the robot links are projected onto the coordinates to generate additional measures of safety. The safety index is used as a constraint in the formulation of the optimization problem so that a collision-free trajectory within a finite time horizon is generated online iteratively for the robot to move toward the desired position. To reduce the computational load for real-time implementation, the formulated optimization problem is further approximated by a quadratic problem. Moreover, a heuristic strategy is proposed to select the active constraints for the next iteration so as to further reduce the computational load. The safety index and the proposed online trajectory generation algorithm are simulated and validated in both a two-link planar robot and a seven-DOF robot in human-robot collaboration and robot-robot collaboration. Simulation results show that the proposed algorithm and robot safety system are capable of generating collision-free and smooth trajectories online.;The proposed algorithm has been extended to consider measurement noise in the agent information. Two possible approaches have been proposed for handling zero-mean Gaussian noise in the agent information.
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