Speaker
Description
In robotics, trajectory generation is a vital topic, especially in the case of planning motion that dynamically changes in response to the robot's interaction with its environment. Generating a feasible trajectory in the task space requires considering the position, velocity, and acceleration bounds imposed on the joint space motion. Due to nonlinear mapping between the task and joint spaces, trajectory generation is non-trivial. It becomes even more involved in the case of redundant manipulators.
A trajectory consists of a path and a time law deciding how fast that path is traversed. For trajectories feasible at the position level are too demanding in terms of velocities or accelerations, trajectory scaling, consisting in slowing down motion, is a reasonable approach leading to fulfillment of the manipulator task. In the simplest case, the whole trajectory—calculated in advance—is uniformly scaled. However, the necessity for off-line calculations and slowing down motion, even in its not-demanding parts, makes this approach impractical.
In this contribution, the gradual development of novel algorithms for trajectory scaling is presented. First, we discuss an algorithm that can be executed online and applies the scaling only to the part of the originally planned trajectory when necessary. The proposed approach analyzes the planned motion in a specified prediction horizon. Moreover, the initially planned path and velocity profile must be known in advance only within this horizon, allowing for a dynamic replanning of the robot’s tasks beyond the prediction horizon. For this algorithm, an inverse kinematic (IK) solver is assumed to be available.
Next, considerations are extended to the case of redundant manipulators. Trajectory scaling is combined with solving the IK. We start by formulating redundancy resolution as a quadratic programming (QP) problem with joint accelerations as the decision variables. Equality constraints enforce task space trajectory, whereas joint acceleration, velocity-, and position-level limits are represented by inequality constraints. Supplementary tasks may be incorporated into the goal function.
Then, the QP-based algorithm is enhanced by introducing trajectory scaling for the next control step. Single-step scaling is effective in many situations, but it may be insufficient in the case of more demanding trajectories. Therefore, the algorithm is further improved by including some prediction window inside which the IK problem is solved, and the trajectory can be scaled. As a result, the novel algorithm with real-time capabilities ensures constraints fulfillment, non-uniformly scales the trajectory, and accepts additional tasks to exploit redundancy.
