Method rapidly verifies that a robot will avoid collisions

Method quickly confirms that a robot will stay out of collisions.

This strategy, which is faster and more precise than some options, could be beneficial for robots which communicate with people or work in confined locations.

When an artificial intelligence can grab dishes from a shelf and set on a table, it must guarantee the grip and arm do not collide with anything, perhaps shattering the fine china. A robot's motion planning method often includes "safety check" algorithms that ensure the trajectory is clear of collisions.

However, these algorithms can produce false positives, indicating that a trajectory is safe while in fact the robot would collide with something. In practice, robots typically cannot keep up with alternative false positive prevention methods due to their slowness.

MIT researchers have devised a safety check technique that can prove with 100% accuracy that a robot's trajectory will remain collision-free (provided the robot and environment models are accurate). Their method is It is so exact that it can distinguish between trajectories separated by only millimeters and delivers proof in a matter of seconds.

However, users do not have to take the researchers' word for it; the mathematical proof created by this technique can be rapidly verified using relatively easy algebra.

The researchers used a particular algorithmic technique known as sum-of-squares programming, which they customized to efficiently address the safety check problem. The use of sum-of-squares programming allows their method to be applied to a wide range of complex motions.

This strategy may be particularly beneficial for robots that must move quickly to avoid collisions in congested environments, such as food preparation robots in a commercial kitchen. It is also well-suited for circumstances when robot collisions may cause injuries, such as at home.Health robots that tend to elderly and sick individuals.

Through this research, we showed that theoretically basic techniques can be used to solve some challenging problems. While it does not solve every problem, sum-of-squares programming is a potent algorithmic idea that, when applied properly, can solve some fairly nontrivial problems "Lead author of a paper on the technique and graduate student in electrical the fields of computer science and engineering , Alexandre Amice, agrees.

Amice works on the article alongside Peter Werner, another EECS graduate student, and senior author Russ Tedrake, the Toyota Professor of EECS, Aeronautics and Astronautics, and Mechanical Engineering and a a participant in the AI and Computer Science Experimental. The International Conference on Robotics and AI will have a presentation of this study.

Validating Security

Many known approaches for evaluating whether a robot's planned motion is collision-free involve simulating the trajectory and checking every few seconds to see if the robot strikes anything. However, static safety tests cannot predict whether the robot will crash with anything in the intervening seconds.

This may not be an issue for a robot walking around an open space with few barriers, but for robots doing complex jobs in tiny locations, a few seconds of motion can make a significant difference.


Conceptually, one technique to demonstrate that a robot is not on its way to a collision is to hold out a piece of paper that separates the robot from any impediments in its path. In mathematics, this sheet of paper is known as a hyperplane. Many safety check methods generate the hyperplane at a single moment in time. However, each time the robot moves, a new hyperplane must be computed in order to execute the safety check.

Instead of focusing on one hyperplane at a time, this new technique develops a hyperplane function that moves with the robot, allowing it to demonstrate that a whole trajectory is collision-free.

The researchers employed sum-of-squares programming, an algorithmic toolbox that may successfully convert a static problem into a function. This function represents a mathematical equation that indicates the location of the hyperplane at each intersection on the suggested path in order to prevent collisions.

Sum-of-squares can help the optimization software locate a family of collision-free hyperplanes. Frequently, sum-of-squares is considered substantial optimization that is best suited for offline use, but the researchers have demonstrated that it is incredibly precise and efficient for this particular application.

The challenge here was figuring out how to use sum-of-squares in our particular situation.The most challenging aspect of the assignment was creating the initial formulation. If I don't want my robot to collide with anything, what does that imply mathematically, and can the computer provide an answer?" Amice explains.

Lastly, sum-of-squares produces a function that is the sum of several squared numbers, as the name suggests. The function is always positive since the square of any number has a positive value.

Trust But Check

A human may readily confirm that the hyperplane function is positive, meaning the trajectory is collision-free, by double-checking that it contains squared values, according to Amice.

The mathematical certifier is only as good as the user's model of the robot and surroundings, even though the approach certifies with perfect accuracy.

He goes on, "This approach has the really nice feature that the proofs are really easy to interpret, so you can check it yourself and don't have to trust me that I coded it right."

They validated that intricate motion plans for robots with one and two arms were collision-free in a simulation to evaluate their methodology. Their technique only required a few hundred milliseconds at its slowest to produce a proof, which makes it considerably quicker than some other methods.

This new finding presents a fresh method for confirming that a complicated robot manipulator route is collision-free by deftly utilizing mathematical optimization techniques to create remarkably quick (and publicly accessible) software. According to Dan Halperin, a Tel Aviv University computer science professor who was not involved in the study, "this result opens the door to several intriguing directions of furtherstudy," despite the fact that it does not currently provide a complete answer for rapid trajectory planning in crowded environments.

Their method is too slow to be included straight into a robot motion planning loop, even though it is quick enough to be employed as a last safety check in some real-world scenarios. According to Amice, choices must be taken in microseconds.

When the robot is far from any items it might collide with, for example, or in other circumstances where safety checks are not necessary, the researchers intend to expedite their approach. Additionally, they wish to test out more specialized, potentially faster optimization algorithms.

Because their routes are generated with inaccurate estimations, robots frequently encounter difficulties when they scrape barriers. By carefully leveraging sophisticated techniques from computational algebraic geometry, Amice, Werner, and Tedrake have come to the rescue with a potent new algorithm to ensure that robots never overstep their bounds," says Steven LaValle, professor in the Faculty of Information Technology and Electrical Engineering at the University of Oulu in Finland not working on this project.