Direct optimal control techniques, relying on numerical methods for constrained optimization, are typically used in trajectory planning tasks in high-dimensional spaces. However, general-purpose solvers often fail to ...
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Direct optimal control techniques, relying on numerical methods for constrained optimization, are typically used in trajectory planning tasks in high-dimensional spaces. However, general-purpose solvers often fail to find a feasible solution when facing cluttered environments. Sampling- or graph-based methods, instead, can explore complex configuration spaces but struggle with dynamic constraints. Here, we propose to combine dynamic programming (DP) and derivative-based methods to reliably solve trajectory planning problems. Specifically, we exploit DP to generate a sequence of waypoints in a low-dimensional space, which are then encoded as pointwise path constraints for a high-dimensional trajectory, whose constraint violations are then represented as a penalty within the Bellman equation to recompute the waypoints. This iterative approach, alternating path and trajectory optimization, avoids both the curse of dimensionality for DP and problematic nonconvexities (such as obstacles) for motion planning. We demonstrate our strategy using numerical experiments on a six-degree-of-freedom robotic manipulator moving in a confined space.
Obstacle avoidance is an essential characteristic of autonomous driving cars. This paper presents a new method for efficiently determining possible routes that a vehicle can follow for overtaking obstacles and classif...
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ISBN:
(纸本)9798350358513;9798350358520
Obstacle avoidance is an essential characteristic of autonomous driving cars. This paper presents a new method for efficiently determining possible routes that a vehicle can follow for overtaking obstacles and classifying them into different topology classes of paths. Impossible routes are eliminated based on the physical constraints of the vehicle. To evaluate each topology class and pick the one with the lowest cost as the globally optimal path, we run several topology-aided nonlinear programming (NLP) problems. For each topologyaided NLP problem to overtake the obstacles from the prespecified side determined by the topology class, corresponding auxiliary halfspace constraints are activated in the optimization problem. Through simulation results and comparisons with a standard NLP planner, we show that the overall computation time for solving several topology-aided NLP problems is faster than that of the standard NLP planner. Additionally, in complex driving scenarios, where the standard planner gets stuck in a sub-optimal solution due to internal faults or a local optimum, our proposed topology-aided planner can still find the globally optimal path.
A dynamic method to solve the general nonlinear programming (NLP) problem, inspired by the Lyapunov continuous-time dynamics stability theory in the control field, is proposed. The optimal solution is regarded as the ...
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ISBN:
(纸本)9798350387780;9798350387797
A dynamic method to solve the general nonlinear programming (NLP) problem, inspired by the Lyapunov continuous-time dynamics stability theory in the control field, is proposed. The optimal solution is regarded as the stable equilibrium point of a finite-dimensional dynamic system and solved in an asymptotic manner. Under the premise that the Karush-Kuhn-Tucker (KKT) optimality condition exists, the Dynamic Optimization Equation (DOE), which has the same dimension to that of the optimization parameter vector, is established within the feasible region and its solution will converge to the optimal solution of the NLP globally. The expressions of the Lagrange multipliers and the KKT multipliers during the entire optimization process are also derived. Using the matrix pseudo-inverse, the DOE is valid even without the linearly independent regularity requirement on the nonlinear constraints. Via the control based method, it is shown that the NLP may be transformed to the Initial-value Problem (IVP) to be solved efficiently, with mature ordinary differential equation integration methods.
We analyze the sample complexity of single-loop quadratic penalty and augmented Lagrangian algorithms for solving nonconvex optimization problems with functional equality constraints. We consider three cases, in all o...
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We analyze the sample complexity of single-loop quadratic penalty and augmented Lagrangian algorithms for solving nonconvex optimization problems with functional equality constraints. We consider three cases, in all of which the objective is stochastic, that is, an expectation over an unknown distribution that is accessed by sampling. The nature of the equality constraints differs among the three cases: deterministic and linear in the first case, deterministic and nonlinear in the second case, and stochastic and nonlinear in the third case. Variance reduction techniques are used to improve the complexity. To find a point that satisfies e-approximate first-order conditions, we require (O) over tilde (epsilon(-3)) complexity in the first case, (O) over tilde (epsilon(-4)) in the second case, and (O) over tilde(epsilon(-5)) in the third case. For the first and third cases, they are the first algorithms of "single loop" type that also use O(1) samples at each iteration and still achieve the best-known complexity guarantees.
Arterial-branch intersections are important components of urban road network but are greatly ignored of its role in maintaining an efficient traffic operation in regional networks. Arterial-branch intersections are ge...
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Arterial-branch intersections are important components of urban road network but are greatly ignored of its role in maintaining an efficient traffic operation in regional networks. Arterial-branch intersections are generally featured with significant fluctuations in the flow ratio of the branch road to the arterial road. So, in order to adapt the signal timing to this kind of intersection, an optimization control algorithm based on fuzzy control and nonlinear programming (FCNP) was proposed. To verify this optimization algorithm, the Python and Vissim joint simulation was employed. Prior to the simulation, traffic flow data were collected in 12 consecutive hours at an arterial-branch intersection in China. The simulation results show that, after signal timing optimization with FCNP, the average vehicle queue length and delay reduced 25.8% and 17.3%, respectively, when compared with the performance of the traffic-actuated control, which also outperformed previous equivalent research. Besides, the overall operation of the intersection was verified to be greatly improved and stabilized by using the proposed algorithm. The findings of this study provide a reasonable solution of distributing the right-of-way at arterial-branch intersections and suggest the advantage of combining fuzzy control and nonlinear programming in dealing with the signal timing optimization.
In the note, we present a new approach to numerical analysis of improper mathematical programming problems based on ideas of symmetrically regularization of their Lagrange functions, additionally equipped with barrier...
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In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs)....
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In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score func-tion of IVIFVs to conquer the drawbacks of the existing score functions of IVIFVs. Then, we construct the converted matrix based on the proposed score function of IVIFVs by cal-culating the score value of each IVIFV in the decision matrix (DM) offered by the decision maker (DMK). Then, we construct the NLP model via the obtained converted matrix and the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute given by the DMK. Then, we solve the NLP model to obtain the optimal weight for each attribute. Then, based on the obtained converted matrix and the obtained optimal weight of each attribute, we calculate the weighted score of each alternative. Finally, the alternatives are ranked on the basis of the obtained weighted scores of the alternatives. The larger the weighted score of an alter-native, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. It offers us a very useful approach for MADM in IVIF settings. (c) 2022 Elsevier Inc. All rights reserved.
In the realm of daily life planning, the challenge of optimizing decisions is frequently encountered, with traditional methods often failing to achieve desired outcomes. To address this issue, this research proposes a...
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Peaking CO2 emissions and reaching carbon neutrality create a major role for hydrogen in the transportation field where decarbonization is difficult. Shanxi, as a microcosm of China in the systematic transformation of...
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Peaking CO2 emissions and reaching carbon neutrality create a major role for hydrogen in the transportation field where decarbonization is difficult. Shanxi, as a microcosm of China in the systematic transformation of energy end-use consumption, is selected to investigate the hydrogen energy development forecast for decarbonization in the transportation sector. Multi-supply-demand integrated scenario analysis with nonlinear programming (NLP) model is established to analyze hydrogen energy deployment in varied periods and regions under minimum environmental, energy and economic objectives, to obtain CO2 emission reduction potential. Results reveal that green hydrogen contributes most to low- carbon hydrogen development strategies. In high-hydrogen demand scenarios, carbon emission reduction potential is significantly higher under environmental objectives, esti- mated at 297.68 x 104-848.12 x 104 tons (2025-2035). The work provides a strategy to forecast hydrogen energy deployment for transportation decarbonization, being of vital significant guide for planning of hydrogen energy transportation in other regions. (c) 2022 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.
In this paper, the automatic pricing and replenishment decision-making problem for vegetable category goods is studied. Using the K-means clustering model, random forest, LSTM long and short-term memory model, and non...
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