Staircase Localization for Autonomous Exploration in Urban Environments

A staircase localization method is proposed for robots to explore urban environments autonomously. The proposed method employs a modular design in the form of a cascade pipeline consisting of three modules of stair detection, line segment detection, and stair localization modules. The stair detection module utilizes an object detection algorithm based on deep learning to generate a region of interest (ROI). From the ROI, line segment features are extracted using a deep line segment detection algorithm. The extracted line segments are used to localize a staircase in terms of position, orientation, and stair direction. The stair detection and localization are performed only with a single RGB-D camera. Each component of the proposed pipeline does not need to be designed particularly for staircases, which makes it easy to maintain the whole pipeline and replace each component with state-of-the-art deep learning detection techniques. The results of real-world experiments show that the proposed method can perform accurate stair detection and localization during autonomous exploration for various structured and unstructured upstairs and downstairs with shadows, dirt, and occlusions by artificial and natural objects.

Parameterized Convex Minorant for Objective Function Approximation in Amortized Optimization

Parameterized convex minorant (PCM) method is proposed for the approximation of the objective function in amortized optimization. In the proposed method, the objective function approximator is expressed by the sum of a PCM and a nonnegative gap function, where the objective function approximator is bounded from below by the PCM convex in the optimization variable. The proposed objective function approximator is a universal approximator for continuous functions, and the global minimizer of the PCM attains the global minimum of the objective function approximator. Therefore, the global minimizer of the objective function approximator can be obtained by a single convex optimization. As a realization of the proposed method, extended parameterized log-sum-exp network is proposed by utilizing a parameterized log-sum-exp network as the PCM. Numerical simulation is performed for non-parameterized-convex objective function approximation and for learning-based nonlinear model predictive control to demonstrate the performance and characteristics of the proposed method. The simulation results support that the proposed method can be used to learn objective functions and to find the global minimizer reliably and quickly by using convex optimization algorithms.

Parametrized Convex Universal Approximators for Decision-Making Problems

Parametrized max-affine (PMA) and parametrized log-sum-exp (PLSE) networks are proposed for general decision-making problems. The proposed approximators generalize existing convex approximators, namely, max-affine (MA) and log-sum-exp (LSE) networks, by considering function arguments of condition and decision variables and replacing the network parameters of MA and LSE networks with continuous functions with respect to the condition variable. The universal approximation theorem of PMA and PLSE is proven, which implies that PMA and PLSE are shape-preserving universal approximators for parametrized convex continuous functions. Practical guidelines for incorporating deep neural networks within PMA and PLSE networks are provided. A numerical simulation is performed to demonstrate the performance of the proposed approximators. The simulation results support that PLSE outperforms other existing approximators in terms of minimizer and optimal value errors with scalable and efficient computation for high-dimensional cases.