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

Abstract

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.

Two Stage Path Planning Method for Co-Worked Double Industrial Robots

“…Chen and Song [18] presented a realtime motion planning and control design of a robotic arm for human-robot collaborative safety. Liu et al [19] proposed a trajectory optimization technique by gradientbased optimization method, which can effectively optimize the robot trajectory under various task constraints. Tang et al [20] presented a coevolution-based particle swarm optimization method to cope with the multi-robot path planning issue.…”

“…is the optimal position of ith particle, 1 1 , k g best − X is the global optimal position of all the particles, c1 and c2 are the learning factor of particle, ω is the inertia weight, r1 and r2 are the random number within 0 and 1. min V and max V are the permissive minimum and maximum of particle speed updating. The updating principle of individual and global optimal position is shown in equation (19) and equation (20), respectively.…”

Reactive Neural Path Planning with Dynamic Obstacle Avoidance in a Condensed Configuration Space

“…Thus, the complexity of path planning in the Cspace significantly increases for robots with many DOFs and cluttered environments. In this case, traditional path planning algorithms are very inefficient as they suffer the curse of 1 All authors are with FZI Research Center for Information Technology, 76131 Karlsruhe, Germany steffen@fzi.de dimensionality. Particularly, complete and optimal search algorithms such as Wavefront, Dijkstra's or A* struggle to provide solutions for more than 3D within a reasonable amount of computation time.…”

“…Particularly, complete and optimal search algorithms such as Wavefront, Dijkstra's or A* struggle to provide solutions for more than 3D within a reasonable amount of computation time. Sample-based planners try to reduce the computational burden using random samples in the C-space and have become the mainstream method for robots with many DOF [1]. However, their computational costs are still exponentially increasing with the number of DOF and especially when it comes to dynamically changing environments or narrow passages, the conventional samplebased planners have difficulties in online applications [2], [3], [4], [5].…”