Efficient trajectory optimization using a sparse model

Abstract

The "timed elastic band" approach optimizes robot trajectories by subsequent modification of an initial trajectory generated by a global planner. The objectives considered in the trajectory optimization include but are not limited to the overall path length, trajectory execution time, separation from obstacles, passing through intermediate way points and compliance with the robots dynamic, kinematic and geometric constraints. "Timed elastic bands" explicitly consider spatialtemporal aspects of the motion in terms of dynamic constraints such as limited robot velocities and accelerations. The trajectory planning operates in real time such that "timed elastic bands" cope with dynamic obstacles and motion constraints. The "timed elastic band problem" is formulated as a scalarized multi-objective optimization problem. Most objectives are local and relate to only a small subset of parameters as they only depend on a few consecutive robot states. This local structure results in a sparse system matrix, which allows the utilization of fast and efficient optimization techniques such as the open-source framework "g2o" for solving "timed elastic band" problems. The "g2o" sparse system solvers have been successfully applied to VSLAM problems. This contribution describes the application and adaptation of the g2o-framework in the context of trajectory modification with the "timed elastic band". Results from simulations and experiments with a real robot demonstrate that the implementation is robust and computationally efficient.

Golf cart prototype development and navigation simulation using ROS and Gazebo

“…We have used the package teb_local_planner 8 , as a local planner, which relies on the method called Timed Elastic Band [13][14][15]. This approach is extended to capture the specific constraints and objectives, which are appropriate for emergency manoeuvres in critical situations [16].…”

Dynamic Channel: A Planning Framework for Crowd Navigation

“…The same problem also exists in other planning methods. For Elastic Band [17], Timed Elastic Band [18] and spline-based planners [19], the initial guess determines path partition, which is based on the static assumption. Ultimately, treating static and dynamic obstacles separately has the advantage of being efficient and probabilistically complete.…”

Global and Local Path Planning Study in a ROS-Based Research Platform for Autonomous Vehicles

“…All of them create intermediate waypoints following the generated trajectory. The selected method for local planning is Time Elastic Bands [15,20] which consists of deforming the initial global plan considering the kinematic model of the vehicle and updating the local path based on dynamic obstacles or the possible deviation from the path. This method has been selected because of the integration of the trajectory planning and obstacle detection with avoidance at low computational cost fulfilling the requirements of the local planner in the research platform iCab.…”