On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions on Robotics (TRO) 201

Chance-Constrained AC Optimal Power Flow Integrating HVDC Lines and Controllability

The integration of large-scale renewable generation has major implications on the operation of power systems, two of which we address in this work. First, system operators have to deal with higher degrees of uncertainty due to forecast errors and variability in renewable energy production. Second, with abundant potential of renewable generation in remote locations, there is an increasing interest in the use of High Voltage Direct Current lines (HVDC) to increase transmission capacity. These HVDC transmission lines and the flexibility and controllability they offer must be incorporated effectively and safely into the system. In this work, we introduce an optimization tool that addresses both challenges by incorporating the full AC power flow equations, chance constraints to address the uncertainty of renewable infeed, modelling of point-to-point HVDC lines, and optimized corrective control policies to model the generator and HVDC response to uncertainty. The main contributions are twofold. First, we introduce a HVDC line model and the corresponding HVDC participation factors in a chance-constrained AC-OPF framework. Second, we modify an existing algorithm for solving the chance-constrained AC-OPF to allow for optimization of the generation and HVDC participation factors. Using realistic wind forecast data, for 10 and IEEE 39 bus systems with HVDC lines and wind farms, we show that our proposed OPF formulation achieves good in- and out-of-sample performance whereas not considering uncertainty leads to high constraint violation probabilities. In addition, we find that optimizing the participation factors reduces the cost of uncertainty significantly

Guidance methods for low-thrust space vehicles Cumulative progress report, 1 Jan. 1969 - 31 Jan. 1970

Guidance and control schemes for optimal low-thrust Earth-Mars transfer mission

Linear Hamilton Jacobi Bellman Equations in High Dimensions

The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent results in the structure of the HJB, and its reduction to a linear Partial Differential Equation (PDE), with methods based on low rank tensor representations, known as a separated representations, to address the curse of dimensionality. The result is an algorithm to solve optimal control problems which scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finite-horizon, average cost, and first-exit settings. The method is demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with system dimension two, six, and twelve respectively.Comment: 8 pages. Accepted to CDC 201