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Architecture
Published in Hanky Sjafrie, Introduction to Self-Driving Vehicle Technology, 2019
Route planning typically uses special algorithms for solving a common graph theory problem called the shortest path problem. The problem can be defined as finding the shortest path between two nodes in a graph. One of the best-known shortest path algorithms is Dijkstra’s algorithm [6] as shown in Figure 4.1. The algorithm starts by initializing the distance value of all nodes to infinity. For all directly reachable nodes from the starting node a new distance value or cost is calculated, and the value is updated if the distance is shorter. This process iterates through the entire graph until all nodes have been traversed. The shortest path to any destination can now be determined by summing the cost of the node and the set of registered edges to reach that node. Faster algorithms, such as Contraction Hierarchies [9], perform some precomputation steps to speed up the process.
Online directed-structural change-point detection: A segment-wise time-varying dynamic Bayesian network approach
Published in IISE Transactions, 2023
Set the memory size of L-BFGS to be p withfor maximum time lag m and node number n, the precomputation time (computation of Hessian matrix) is only, and each coordinate update isdue to the computation of, where q is the number of inner iterations (Zhonget al., 2014). Furthermore, since we are using sparsity regularization, we can further speed up the algorithm based on subgradients by aggressively shrinking. The shrinking strategy excludes the remaining dimensions whose values are zeros from being updated. With the updates restricted to the active set S, all dependencies of the complexity onbecomes, which is substantially smaller. Hence, the overall complexity of L-BFGS update is. Set the number of outer iterations to befor the augmented Lagrangian in Algorithm 1. The overall complexity of L-BFGS-B nested in PELT is. Then the overall time complexity of ONSMART isat each time point.
Set-based fast gradient projection algorithm for model predictive control of grid-tied power converters
Published in Automatika, 2023
Renato Babojelić, Bruno Vilić Belina, Šandor Ileš, Jadranko Matuško
The paper is divided into sections as follows: Section 2 introduces the mathematical model of a grid-tied two-level inverter with an LCL filter; Section 3 presents a set-based model predictive control algorithm; and Section 4 presents a modified fast gradient method for solving the MPC optimization problem. Section 5 describes the LPV model and needed modifications to the MPC algorithm to allow for the robust handling of variation in grid inductance, and Section 6 describes the offline precomputation of data needed for implementation in embedded systems. Section 7 shows the simulation results of a proposed algorithm, and Section 8 concludes the paper.
Real-time walking step timing adaptation by restricting duration decision for the first footstep
Published in Advanced Robotics, 2020
Marcos R. O. A. Maximo, Carlos H. C. Ribeiro, Rubens J. M. Afonso
This precomputation is carried out by the function shown in Algorithm 1, where the inputs , , , , , and represent the reference rotational speed, a boolean variable indicating if the left foot is the swing foot, another boolean indicating if the robot is in double support, the number of timesteps the robot has been on the current footstep, the current footstep rotation, and the swing foot rotation, respectively. The other variables have the following meaning: denotes the support foot rotation of the future footstep j when the first footstep lasts m timesteps, is the maximum allowed rotational speed, is the time the footstep is allowed to move, and is a predefined step duration which was selected to attain a secondary objective such as energetic expenditure minimization [20]. Finally, the function has the following definition: Notice that to avoid collision between the feet, the swing foot is only allowed to rotate if it is moving away from the support foot, which is verified by the logic . Furthermore, to account for the fact that the swing foot is only allowed to rotate every other step, the swing foot tries to attain an average speed of considering two consecutive footsteps, as seen in lines 7 and 11 of Algorithm 1.