Robotic manipulators are often designed with more actuated degrees-of-freedom than required to fully control an end effector's position and orientation. These "redundant" manipulators can allow infinite joint configurations that satisfy a particular task-space position and orientation, providing more possibilities for the manipulator to traverse a smooth collision-free trajectory. However, finding such a trajectory is non-trivial because the inverse kinematics for redundant manipulators cannot typically be solved analytically. Many strategies have been developed to tackle this problem, including Jacobian pseudo-inverse method, rapidly-expanding-random tree (RRT) motion planning, and quadratic programming (QP) based methods. Here, we present a flexible inverse kinematics-based QP strategy (iKinQP). Because it is independent of robot dynamics, the algorithm is relatively light-weight, and able to run in real-time in step with torque control. Collisions are defined as kinematic trees of elementary geometries, making the algorithm agnostic to the method used to determine what collisions are in the environment. Collisions are treated as hard constraints which guarantees the generation of collision-free trajectories. Trajectory smoothness is accomplished through the QP optimization. Our algorithm was evaluated for computational efficiency, smoothness, and its ability to provide trackable trajectories. It was shown that iKinQP is capable of providing smooth, collision-free trajectories at real-time rates.

翻译：机械臂的驱动自由度通常多于完全控制末端执行器位姿所需的自由度。这类“冗余”机械臂存在无限组满足特定任务空间位姿的关节构型，为机械臂生成平滑无碰撞轨迹提供了更多可能性。然而，由于冗余机械臂的逆运动学通常无法解析求解，寻找此类轨迹具有相当的难度。目前已发展出多种解决方案，包括雅可比伪逆法、快速扩展随机树(RRT)运动规划以及基于二次规划的方法。本文提出了一种灵活的逆运动学二次规划策略(iKinQP)。该算法独立于机器人动力学模型，计算量相对较小，能够实时运行并与力矩控制保持同步。算法将碰撞定义为基本几何体的运动学树结构，使其与环境中碰撞检测的具体方法无关。通过将碰撞设置为硬约束条件，可确保生成无碰撞轨迹，而轨迹平滑性则通过二次规划优化实现。我们从计算效率、轨迹平滑度及可跟踪性三个维度评估了算法性能。实验证明，iKinQP能以实时速率生成平滑的无碰撞轨迹。