Trajectory optimization o↵ers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous di↵erential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization prob- lem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of B ́ezier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap round- ing of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.
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On avoiding Moving Objects for indoor autonomous quadrotors
A mini quadrotor can be used in many applications, such as indoor airborne surveillance, payload delivery, and warehouse monitoring. In these applications, vision-based autonomous navigation is one of the most interesting research topics because precise navigation can be implemented based on vision analysis. However, pixel-based vision analysis approaches require a high-powered computer, which is inappropriate to be attached to a small indoor quadrotor. This paper proposes a method called the Motion-vector-based Moving Objects Detection. This method detects and avoids obstacles using stereo motion vectors instead of individual pixels, thereby substantially reducing the data processing requirement. Although this method can also be used in the avoidance of stationary obstacles by taking into account the ego-motion of the quadrotor, this paper primarily focuses on providing our empirical verification on the real-time avoidance of moving objects.
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- Award ID(s):
- 1521153
- NSF-PAR ID:
- 10021678
- Date Published:
- Journal Name:
- 2016 IEEE International Conference on Automation Science and Engineering (CASE),
- Page Range / eLocation ID:
- 503 to 508
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/COASE.2016.7743447
