Motion Planning for Autonomous Driving With Extended Constrained Iterative LQR

Autonomous driving planning is a challenging problem when the environment is complicated. It is difficult for the planner to find a good trajectory that navigates autonomous cars safely with crowded surrounding vehicles. To solve this complicated problem, a fast algorithm that generates a high-quality, safe trajectory is necessary. Constrained Iterative Linear Quadratic Regulator (CILQR) is appropriate for this problem, and it successfully generates the required trajectory in realtime. However, CILQR has some deficiencies. Firstly, CILQR uses logarithmic barrier functions for hard constraints, which will cause numerical problems when the initial trajectory is infeasible. Secondly, the convergence speed is slowed with a bad initial trajectory, which might violate the real-time requirements. To address these problems, we propose the extended CILQR by adding two new features. The first one is using relaxed logarithmic barrier functions instead of the standard logarithmic barrier function to prevent numerical issues. The other one is adding an efficient initial trajectory creator to generate a good initial trajectory. Moreover, this initial trajectory helps CILQR to converge to a desired local optimum. These new features extend CILQR’s usage to more practical autonomous driving applications. Simulation results show that our algorithm is effective in challenging driving environments.

A log-barrier Newton-CG method for bound constrained optimization with complexity guarantees

We describe an algorithm based on a logarithmic barrier function, Newton’s method and linear conjugate gradients that seeks an approximate minimizer of a smooth function over the non-negative orthant. We develop a bound on the complexity of the approach, stated in terms of the required accuracy and the cost of a single gradient evaluation of the objective function and/or a matrix-vector multiplication involving the Hessian of the objective. The approach can be implemented without explicit calculation or storage of the Hessian.

FPGA Implementation of an Improved Reconfigurable FSMIM Architecture Using Logarithmic Barrier Function Based Gradient Descent Approach

Recently, the Reconfigurable FSM has drawn the attention of the researchers for multistage signal processing applications. The optimal synthesis of Reconfigurable finite state machine with input multiplexing (Reconfigurable FSMIM) architecture is done by the iterative greedy heuristic based Hungarian algorithm (IGHA). The major problem concerning IGHA is the disintegration of a state encoding technique. This paper proposes the integration of IGHA with the state assignment using logarithmic barrier function based gradient descent approach to reduce the hardware consumption of Reconfigurable FSMIM. Experiments have been performed using MCNC FSM benchmarks which illustrate a significant area and speed improvement over other architectures during field programmable gate array (FPGA) implementation.

Lower Bound Axisymmetric Limit Analysis Using Drucker–Prager Yield Cone and Simulation with Mohr–Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker–Prager (D–P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D–P yield cone with the Mohr–Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors Nc, Nq and Nγ have been computed, as a function of ϕ, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

NEWTON FLOW AND INTERIOR POINT METHODS IN LINEAR PROGRAMMING

We study the geometry of the central paths of linear programming theory. These paths are the solution curves of the Newton vector field of the logarithmic barrier function. This vector field extends to the boundary of the polytope and we study the main properties of this extension: continuity, analyticity, singularities.