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 convert 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.

中文翻译：

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通过线性约束二次规划为机器人运动规划创建更好的无碰撞轨迹

已经提出了许多基于概率采样的运动规划算法，以在有障碍物的环境中为机器人创建路径。由于采样的随机性，它们可以有效地计算由位于具有概率完整性的配置空间中的段组成的无碰撞路径。然而，这个特性也使得轨迹有一些不必要的冗余或生涩的运动，需要优化。对于大多数机器人应用，轨迹应该是短的、平滑的并且远离障碍物。本文提出了一种新的轨迹优化技术，将多边形无碰撞路径转换为平滑路径，并且可以处理包含各种任务约束的轨迹。该技术通过在轨迹参数空间中的二次规划去除冗余运动，并将避碰条件转化为线性约束，确保轨迹绝对安全。此外，该技术使用投影算子来实现轨迹的优化，这些轨迹受到一些硬运动学约束，例如保持一杯水直立或与双机器人协调操作。与其他轨迹优化方法相比，实验结果证明了该方法的可行性和有效性。