scholarly journals A New Noninterior Continuation Method for Solving a System of Equalities and Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jianguang Zhu ◽  
Binbin Hao
Keyword(s):  
Numerical Experiments ◽  
Continuation Method ◽  
Accumulation Point ◽  
Nonsmooth Equations ◽  
Smoothing Technique ◽  
Minimum Function ◽  
Iteration Sequence ◽  
Slack Variables ◽  
Smooth Operator

By using slack variables and minimum function, we first reformulate the system of equalities and inequalities as a system of nonsmooth equations, and, using smoothing technique, we construct the smooth operator. A new noninterior continuation method is proposed to solve the system of smooth equations. It shows that any accumulation point of the iteration sequence generated by our algorithm is a solution of the system of equalities and inequalities. Some numerical experiments show the feasibility and efficiency of the algorithm.

scholarly journals A New Smoothing Nonlinear Conjugate Gradient Method for Nonsmooth Equations with Finitely Many Maximum Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yuan-yuan Chen ◽  
Shou-qiang Du
Keyword(s):  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Complementarity Problems ◽  
Accumulation Point ◽  
Merit Function ◽  
New Method ◽  
Nonsmooth Equations ◽  
Nonlinear Conjugate Gradient Method ◽  
Nonlinear Conjugate Gradient

The nonlinear conjugate gradient method is of particular importance for solving unconstrained optimization. Finitely many maximum functions is a kind of very useful nonsmooth equations, which is very useful in the study of complementarity problems, constrained nonlinear programming problems, and many problems in engineering and mechanics. Smoothing methods for solving nonsmooth equations, complementarity problems, and stochastic complementarity problems have been studied for decades. In this paper, we present a new smoothing nonlinear conjugate gradient method for nonsmooth equations with finitely many maximum functions. The new method also guarantees that any accumulation point of the iterative points sequence, which is generated by the new method, is a Clarke stationary point of the merit function for nonsmooth equations with finitely many maximum functions.

scholarly journals Toward a More Complete, Flexible, and Safer Speed Planning for Autonomous Driving via Convex Optimization

2018 ◽  
Author(s):  
Yu Zhang ◽  
Huiyan Chen ◽  
Steven L. Waslander ◽  
Tian Yang ◽  
Sheng Zhang ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Case Studies ◽  
Numerical Experiments ◽  
State Of The Art ◽  
Autonomous Driving ◽  
Dynamic Environments ◽  
Global Optimality ◽  
Slack Variables ◽  
Fixed Path ◽  
Planning Problems

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

scholarly journals Toward a More Complete, Flexible, and Safer Speed Planning for Autonomous Driving via Convex Optimization

2018 ◽  
Author(s):  
Yu Zhang ◽  
Huiyan Chen ◽  
Steven L. Waslander ◽  
Tian Yang ◽  
Sheng Zhang ◽  
...  
Keyword(s):  
Convex Optimization ◽  
Case Studies ◽  
Numerical Experiments ◽  
State Of The Art ◽  
Autonomous Driving ◽  
Dynamic Environments ◽  
Global Optimality ◽  
Slack Variables ◽  
Fixed Path ◽  
Planning Problems

In this paper, we present a complete, flexible and safe convex-optimization-based method to solve speed planning problems over a fixed path for autonomous driving in both static and dynamic environments. Our contributions are five fold. First, we summarize the most common constraints raised in various autonomous driving scenarios as the requirements for speed planner developments and metrics to measure the capacity of existing speed planners roughly for autonomous driving. Second, we introduce a more general, flexible and complete speed planning mathematical model including all the summarized constraints compared to the state-of-the-art speed planners, which addresses limitations of existing methods and is able to provide smooth, safety-guaranteed, dynamic-feasible, and time-efficient speed profiles. Third, we emphasize comfort while guaranteeing fundamental motion safety without sacrificing the mobility of cars by treating the comfort box constraint as a semi-hard constraint in optimization via slack variables and penalty functions, which distinguishes our method from existing ones. Fourth, we demonstrate that our problem preserves convexity with the added constraints, thus global optimality of solutions is guaranteed. Fifth, we showcase how our formulation can be used in various autonomous driving scenarios by providing several challenging case studies in both static and dynamic environments. A range of numerical experiments and challenging realistic speed planning case studies have depicted that the proposed method outperforms existing speed planners for autonomous driving in terms of constraint type covered, optimality, safety, mobility and flexibility.

Controllable Compliance Joint For Human Oriented Robots

2013 ◽  
Vol 43 (1) ◽  
pp. 47-60
Author(s):  
Mihail Tsveov ◽  
Dimitar Chakarov
Keyword(s):  
Numerical Experiments ◽  
Position Control ◽  
Joint Stiffness ◽  
Joint Motion ◽  
Compliance Control ◽  
Leaf Springs ◽  
Antagonistic Actuation

Abstract In the paper, different approaches for compliance control for human oriented robots are revealed. The approaches based on the non- antagonistic and antagonistic actuation are compared. In addition, an approach is investigated in this work for the compliance and the position control in the joint by means of antagonistic actuation. It is based on the capability of the joint with torsion leaf springs to adjust its stiffness. Models of joint stiffness are presented in this paper with antagonistic and non-antagonistic influence of the spring forces on the joint motion. The stiffness and the position control possibilities are investigated and the opportunity for their decoupling as well. Some results of numerical experiments are presented in the paper too.

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