scholarly journals Creating Better Collision-Free Trajectory for Robot Motion Planning by Linearly Constrained Quadratic Programming

2021 ◽  
Vol 15 ◽  
Author(s):  
Yizhou Liu ◽  
Fusheng Zha ◽  
Mantian Li ◽  
Wei Guo ◽  
Yunxin Jia ◽  
...  

Many algorithms in probabilistic sampling-based motion planning have been proposed to create a path for a robot in an environment with obstacles. Due to the randomness of sampling, they can efficiently compute the collision-free paths made of segments lying in the configuration space with probabilistic completeness. However, this property also makes the trajectories have some unnecessary redundant or jerky motions, which need to be optimized. For most robotics applications, the trajectories should be short, smooth and keep away from obstacles. This paper proposes a new trajectory optimization technique which transforms a polygon collision-free path into a smooth path, and can deal with trajectories which contain various task constraints. The technique removes redundant motions by quadratic programming in the parameter space of trajectory, and converts collision avoidance conditions to linear constraints to ensure absolute safety of trajectories. Furthermore, the technique uses a projection operator to realize the optimization of trajectories which are subject to some hard kinematic constraints, like keeping a glass of water upright or coordinating operation with dual robots. The experimental results proved the feasibility and effectiveness of the proposed method, when it is compared with other trajectory optimization methods.

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sumati Mahajan ◽  
S. K. Gupta ◽  
Izhar Ahmad ◽  
S. Al-Homidan

AbstractQuadratic programming is potentially capable of strategic decision making in real world problems. However, practical problems rarely conform to crisp parameters, and hence the prospects of these problems with inexact parameters are inevitably higher. The existing studies regarding public welfare schemes/ organizations reveal that their objectives end up as minimization of cost functions and are governed by linear or concave quadratic programming problems. The present study proposes a method that can be applied to concave type quadratic objective function subject to linear constraints with inexact parameters. A comparison is also drawn with existing methods to establish its simplicity and efficiency. Further, a numerical example is illustrated, and finally, a waste management problem is formulated and solved using the proposed method.


2019 ◽  
Vol 45 (2) ◽  
pp. 20-23
Author(s):  
Thaker Nayl

Collision avoidance techniques tend to derive the robot away of the obstacles in minimal total travel distance. Most ofthe collision avoidance algorithms have trouble get stuck in a local minimum. A new technique is to avoid local minimum in convexoptimization-based path planning. Obstacle avoidance problem is considered as a convex optimization problem under system state andcontrol constraints. The idea is by considering the obstacles as a convex set of points which represents the obstacle that encloses inminimum volume ellipsoid, also the addition of the necessary offset distance and the modified motion path is presented. In the analysis,the results demonstrated the effectiveness of the suggested motion planning by using the convex optimization technique.


2021 ◽  
Author(s):  
Oskar Weser ◽  
Björn Hein Hanke ◽  
Ricardo Mata

In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimisations with non-linear constraints. Analytical gradients for the transformation between the coordinate systems were derived for the first time, which allows analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimisation was coupled with a Symbolic Algebra package to support arbitrary non-linear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. Sample applications are provided for a number of common chemical reactions and illustrative examples where these new algorithms can be used to automatically produce chemically reasonable structure interpolations, or to perform non-linearly constrained optimisations of molecules.


2019 ◽  
Author(s):  
Shuai Fan ◽  
guangyu he ◽  
Xinyang Zhou ◽  
Mingjian Cui

This paper proposes a Lyapunov optimization-based <a><b> </b></a>online distributed (LOOD) algorithmic framework for active distribution networks with numerous photovoltaic inverters and invert air conditionings (IACs). In the proposed scheme, ADNs can track an active power setpoint reference at the substation in response to transmission-level requests while concurrently minimizing the utility loss and ensuring the security of voltages. In contrast to conventional distributed optimization methods that employ the setpoints for controllable devices only when the algorithm converges, the proposed LOOD can carry out the setpoints immediately relying on the current measurements and operation conditions. Notably, the time-coupling constraints of IACs are decoupled for online implementation with Lyapunov optimization technique. An incentive scheme is tailored to coordinate the customer-owned assets in lieu of the direct control from network operators. Optimality and convergency are characterized analytically. Finally, we corroborate the proposed method on a modified version of 33-node test feeder. <div><br></div>


Sign in / Sign up

Export Citation Format

Share Document