Method rapidly verifies that a robot will avoid collisions

Good news! A mathematical proof to be collision free! Stay out off my hyperplane!

E.g. poor approximations make robots unsafe! Just a millimeter off, could cause potential scraping by the robot etc.

"... As part of its motion planning process, a robot typically runs “safety check” algorithms that verify its trajectory is collision-free. ...

Now, MIT researchers have developed a safety check technique which can prove with 100 percent accuracy that a robot’s trajectory will remain collision-free (assuming the model of the robot and environment is itself accurate). Their method, which is so precise it can discriminate between trajectories that differ by only millimeters, provides proof in only a few seconds. ...
the mathematical proof generated by this technique can be checked quickly with relatively simple math. ...

Instead, this new technique generates a hyperplane function that moves with the robot, so it can prove that an entire trajectory is collision-free rather than working one hyperplane at a time. ...

“This new result suggests a novel approach to certifying that a complex trajectory of a robot manipulator is collision free, elegantly harnessing tools from mathematical optimization, turned into surprisingly fast (and publicly available) software. While not yet providing a complete solution to fast trajectory planning in cluttered environments, this result opens the door to several intriguing directions of further research,” ..."

From the abstract:

"We present an efficient method for certifying non-collision for piecewise-polynomial motion plans in algebraic reparametrizations of configuration space. Such motion plans include those generated by popular randomized methods including RRTs and PRMs, as well as those generated by many methods in trajectory optimization. Based on Sums-of-Squares optimization, our method provides exact, rigorous certificates of non-collision; it can never falsely claim that a motion plan containing collisions is collision-free. We demonstrate that our formulation is practical for real world deployment, certifying the safety of a twelve degree of freedom motion plan in just over a second. Moreover, the method is capable of discriminating the safety or lack thereof of two motion plans which differ by only millimeters."

Method rapidly verifies that a robot will avoid collisions | MIT News | Massachusetts Institute of Technology Faster and more accurate than some alternatives, this approach could be useful for robots that interact with humans or work in tight spaces.

Certifying Bimanual RRT Motion Plans in a Second