We present a new optimization-based approach for robotic motion planning among obstacles. Like CHOMP (Covariant Hamiltonian Optimization for Motion Planning), our algorithm can be used to find collision-free trajectories from naïve, straight-line initializations that might be in collision. At the core of our approach are (a) a sequential convex optimization procedure, which penalizes collisions with a hinge loss and increases the penalty coefficients in an outer loop as necessary, and (b) an efficient formulation of the no-collisions constraint that directly considers continuous-time safety Our algorithm is implemented in a software package called TrajOpt.We report results from a series of experiments comparing TrajOpt with CHOMP and randomized planners from OMPL, with regard to planning time and path quality. We consider motion planning for 7 DOF robot arms, 18 DOF full-body robots, statically stable walking motion for the 34 DOF Atlas humanoid robot, and physical experiments with the 18 DOF PR2. We also apply TrajOpt to plan curvature-constrained steerable needle trajectories in the SE(3) configuration space and multiple non-intersecting curved channels within 3D-printed implants for intracavitary brachytherapy. Details, videos, and source code are freely available at: http://rll.berkeley.edu/trajopt/ijrr.

Photon avalanching nanoparticles (ANPs) exhibit extremely nonlinear upconverted emission valuable for subdiffraction imaging, nanoscale sensing, and optical computing. Avalanching has been demonstrated with Tm³⁺-, Pr³⁺-, or Nd³⁺-doped nanocrystals, but their emission is limited to a few wavelengths and materials. Here, we utilize Gd³⁺-assisted energy migration to tune the emission wavelengths of Tm³⁺-sensitized ANPs and generate highly nonlinear emission from Eu³⁺, Tb³⁺, Ho³⁺, and Er³⁺ ions. The upconversion intensities of these spectrally discrete ANPs scale with nonlinearity factor s = 10-17 under 1064 nm excitation at power densities as low as 7 kW cm^-2. This strategy for imprinting avalanche behavior on remote emitters can be extended to fluorophores adjacent to ANPs, as we demonstrate with CdS/CdSe/CdS core/shell/shell quantum dots. ANPs with rationally designed energy transfer networks provide the means to transform conventional linear emitters into a highly nonlinear ones, expanding the use of photon avalanching in biological, chemical, and photonic applications.