Stochastic Extended LQR for Optimization-based Motion Planning Under Uncertainty.

We introduce a novel optimization-based motion planner, Stochastic Extended LQR (SELQR), which computes a trajectory and associated linear control policy with the objective of minimizing the expected value of a user-defined cost function. SELQR applies to robotic systems that have stochastic non-linear dynamics with motion uncertainty modeled by Gaussian distributions that can be state- and control-dependent. In each iteration, SELQR uses a combination of forward and backward value iteration to estimate the cost-to-come and the cost-to-go for each state along a trajectory. SELQR then locally optimizes each state along the trajectory at each iteration to minimize the expected total cost, which results in smoothed states that are used for dynamics linearization and cost function quadratization. SELQR progressively improves the approximation of the expected total cost, resulting in higher quality plans. For applications with imperfect sensing, we extend SELQR to plan in the robot's belief space. We show that our iterative approach achieves fast and reliable convergence to high-quality plans in multiple simulated scenarios involving a car-like robot, a quadrotor, and a medical steerable needle performing a liver biopsy procedure.

Virtualized Traffic: reconstructing traffic flows from discrete spatiotemporal data.

We present a novel concept, Virtualized Traffic, to reconstruct and visualize continuous traffic flows from discrete spatiotemporal data provided by traffic sensors or generated artificially to enhance a sense of immersion in a dynamic virtual world. Given the positions of each car at two recorded locations on a highway and the corresponding time instances, our approach can reconstruct the traffic flows (i.e., the dynamic motions of multiple cars over time) between the two locations along the highway for immersive visualization of virtual cities or other environments. Our algorithm is applicable to high-density traffic on highways with an arbitrary number of lanes and takes into account the geometric, kinematic, and dynamic constraints on the cars. Our method reconstructs the car motion that automatically minimizes the number of lane changes, respects safety distance to other cars, and computes the acceleration necessary to obtain a smooth traffic flow subject to the given constraints. Furthermore, our framework can process a continuous stream of input data in real time, enabling the users to view virtualized traffic events in a virtual world as they occur. We demonstrate our reconstruction technique with both synthetic and real-world input.

A method to obtain a near-minimal-volume molecular simulation of a macromolecule, using periodic boundary conditions and rotational constraints.

If the rotational motion of a single macromolecule is constrained during a molecular dynamics simulation with periodic boundary conditions it is possible to perform such simulations in a computational box with a minimal amount of solvent. In this article we describe a method to construct such a box, and test the approach on a number of macromolecules, randomly chosen from the protein databank. The essence of the method is that the molecule is first dilated with a layer of at least half the cut-off radius. For the enlarged molecule a near-densest lattice packing is calculated. From this packing the simulation box is derived. On average, the volume of the resulting box proves to be about 50% of the volume of standard boxes. In test simulations this yields on average a factor of about two in simulation speed.