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Robot motion planning has traditionally been used to avoid collisions when moving a robot arm. Avoiding collisions is important, but many other desirable criteria are often ignored. For example, motions that minimize energy will let the robot extend its battery life. Smoother trajectories may cause less wear on motors and can be more aesthetically appealing. There may be even more useful criteria, like keeping a glass of water upright when moving it around. This summer, Mrinal Kalakrishnan from the Computational Learning and Motor Control Lab at USC worked on a new motion planner called STOMP, which stands for "Stochastic Trajectory Optimization for Motion Planning". This planner can plan paths for high-dimensional robotic systems that are collision-free, smooth, and can simultaneously satisfy task constraints, minimize energy consumption, or optimize other arbitrary criteria. STOMP is derived from gradient-free optimization and path integral reinforcement learning techniques (Policy Improvement with Path Integrals, Theodorou et al, 2010).

Nikki Graziano's intriguing integration of mathematical curves into her photography sparked a Radar discussion about the relationship between mathematics and the real world. Does her work give insight into the nature of mathematics? Or into the nature of the world? And if so, what kind of insight? Mathematically, matching one curve to another isn't a big deal. Given N points, it's trivial to write an N+1 degree equation that passes through all of them. There are many more subtle ways of solving the same problem, with more aesthetically pleasing results: you can use sine functions, wavelets, square waves, whatever you want. Take out a ruler, measure some points, plug them into Mathematica, and in seconds you can generate as many curves as you like. So finding an equation that matches the curve of an artfully trimmed hedge is easy. The question is whether that curve tells us anything, or whether it's just another stupid math trick.