Dynamic Envelopes and Robustly, Continuously Collision-free Trajectories

In an unpredictable real-world environment, how the objects move is usually not known beforehand. Thus, whether a robot trajectory is safely collision-free or not has to be tested on-line based on sensing as the robot moves in the environment and taking into account robot motion uncertainty. The problem is more challenging if the robot has a high degree of freedom, such as a mobile manipulator. In this talk, we introduce a general on-line approach to test if a given trajectory segment of the robot, which can have high-DOF, is continuously collision-free, and moreover, if the trajectory segment is robustly collision-free, that is, if some deviation of the trajectory within certain “tunnel” of the configuration-time space of the robot is also continuously collision-free. Our method is based on the novel concept of dynamic envelopes [1], which takes advantage of progressive sensing over time without predicting motions of obstacles or assuming specific obstacle motion patterns. Assume that every obstacle in the unpredictable environment can have a linear speed no greater than vmax. Let R(C) be the physical region occupied by the robot at configuration C. To test if the robot at configuration C and future time t is collision-free or not, i.e., if the configuration-time point x = (C, t) is collision-free or not, we define a dynamic envelope E(x, τ) as the closed surface surrounding R(C), such that the minimum distance between R(C) and E(x, τ) is vmax(t-τ), for sensing time τ < t. If E(x, τ) is free of obstacle, x= (C, t) is detected collision-free for sure at sensing time τ. As E(x, τ) is a function of τ, this concept facilitates progressive sensing over a period time to detect if (C, t) is surely collision-free or not before time t. Moreover, if the configuration-time point (C, t) is detected collision-free, we will show that a neighborhood of (C, t) is also collision-free. Based on that, we will further introduce an on-line approach to test if a continuous “tunnel” of trajectories in the robot’s configuration-time space is collision-free or not by checking if a set of discrete configuration-time points are collision-free or not [2]. Thus, through the concept of dynamic envelopes, we can achieve on-line testing of whether a trajectory segment is continuously and robustly collision-free or not. This approach can be used by a realtime motion planner, such as the RAMP [3], to plan continuously and robustly collision-free trajectories in unpredictable environment. If a robot has multiple rigid links, a dynamic envelope can be viewed as the union of dynamic envelopes for individual links, which are usually of simple shapes. Therefore, the detection of whether a dynamic envelope intersects an obstacle can be performed quite efficiently via existing fast collision detection algorithms. However, if a robot consists of deformable links, such as a Workshop on Robot Motion Planning: Online, Reactive, and in Real-time 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2012 Vilamoura, Algarve, Portugal, October 7-12, 2012