Accelerating Motion Planning via Optimal Transport

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide smooth solutions is gradient-based trajectory optimization. However, those methods usually suffer from bad local minima, while for many settings, they may be inapplicable due to the absence of easy-to-access gradients of the optimization objectives. In response to these issues, we introduce Motion Planning via Optimal Transport (MPOT) -- a \textit{gradient-free} method that optimizes a batch of smooth trajectories over highly nonlinear costs, even for high-dimensional tasks, while imposing smoothness through a Gaussian Process dynamics prior via the planning-as-inference perspective. To facilitate batch trajectory optimization, we introduce an original zero-order and highly-parallelizable update rule: the Sinkhorn Step, which uses the regular polytope family for its search directions. Each regular polytope, centered on trajectory waypoints, serves as a local cost-probing neighborhood, acting as a \textit{trust region} where the Sinkhorn Step "transports" local waypoints toward low-cost regions. We theoretically show that Sinkhorn Step guides the optimizing parameters toward local minima regions of non-convex objective functions. We then show the efficiency of MPOT in a range of problems from low-dimensional point-mass navigation to high-dimensional whole-body robot motion planning, evincing its superiority compared to popular motion planners, paving the way for new applications of optimal transport in motion planning.Comment: Published as a conference paper at NeurIPS 2023. Project website: https://sites.google.com/view/sinkhorn-step

Barriers to Diffusion in Dendrites and Estimation of Calcium Spread Following Synaptic Inputs

The motion of ions, molecules or proteins in dendrites is restricted by cytoplasmic obstacles such as organelles, microtubules and actin network. To account for molecular crowding, we study the effect of diffusion barriers on local calcium spread in a dendrite. We first present a model based on a dimension reduction approach to approximate a three dimensional diffusion in a cylindrical dendrite by a one-dimensional effective diffusion process. By comparing uncaging experiments of an inert dye in a spiny dendrite and in a thin glass tube, we quantify the change in diffusion constants due to molecular crowding as Dcyto/Dwater = 1/20. We validate our approach by reconstructing the uncaging experiments using Brownian simulations in a realistic 3D model dendrite. Finally, we construct a reduced reaction-diffusion equation to model calcium spread in a dendrite under the presence of additional buffers, pumps and synaptic input. We find that for moderate crowding, calcium dynamics is mainly regulated by the buffer concentration, but not by the cytoplasmic crowding, dendritic spines or synaptic inputs. Following high frequency stimulations, we predict that calcium spread in dendrites is limited to small microdomains of the order of a few microns (<5 μm)

Intrinsic joint kinematic planning. I: Reassessing the Listing's law constraint in the control of three-dimensional arm movements

16 page(s

Simulating Discrete and Rhythmic Multi-joint Human Arm Movements by Optimization of Nonlinear Performance Indices

An optimization approach applied to mechanical linkage models is used to simulate human arm movements. Predicted arm trajectories are the result of minimizing a nonlinear performance index that depends on kinematic or dynamic variables of the movement. A robust optimization algorithm is presented that computes trajectories which satisfy the necessary conditions with high accuracy. It is especially adapted to the analysis of discrete and rhythmic movements. The optimization problem is solved by parameterizing each generalized coordinate (e.g., joint angular displacement) in terms of Jacobi polynomials and Fourier series, depending on whether discrete or rhythmic movements are considered, combined with a multiple shooting algorithm. The parameterization of coordinates has two advantages. First, it provides an initial guess for the multiple shooting algorithm which solves the optimization problem with high accuracy. Second, it leads to a low dimensional representation of discrete and rhythmic movements in terms of expansion coefficients. The selection of a suitable feature space is an important prerequisite for comparison, recognition and classification of movements. In addition, the separate computational analysis of discrete and rhythmic movements is motivated by their distinct neurophysiological realizations in the cortex. By investigating different performance indices subject to different boundary conditions, the approach can be used to examine possible strategies that humans adopt in selecting specific arm motions for the performance of different tasks in a plane and in three-dimensional space