To control humanoid robots, the reference pose of end effector(s) is planned in task space, then mapped into the reference joints by IK. By viewing that problem as approximate quadratic programming (QP), recent QP solvers can be applied to solve it precisely, but iterative numerical IK solvers based on Jacobian are still in high demand due to their low computational cost. However, the conventional Jacobian-based IK usually clamps the obtained joints during iteration according to the constraints in practice, causing numerical instability due to non-smoothed objective function. To alleviate the clamping problem, this study explicitly considers the joint constraints, especially the box constraints in this paper, inside the new IK solver. Specifically, instead of clamping, a mirror descent (MD) method with box-constrained real joint space and no-constrained mirror space is integrated with the Jacobian-based IK, so-called MD-IK. In addition, to escape local optima nearly on the boundaries of constraints, a heuristic technique, called $\epsilon$-clamping, is implemented as margin in software level. Finally, to increase convergence speed, the acceleration method for MD is integrated assuming continuity of solutions at each time. As a result, the accelerated MD-IK achieved more stable and enough fast tracking performance compared to the conventional IK solvers. The low computational cost of the proposed method mitigated the time delay until the solution is obtained in real-time humanoid gait control, achieving a more stable gait.
翻译:为了控制人造机器人, 在任务空间中计划终端效应的参考配置, 然后由 IK 绘制到参考点 。 通过将这一问题视为近似二次编程( QP ), 最近的 QP 解答器可以精确地解决这个问题, 但基于 Jacobian 的迭代数字 IK 解答器由于计算成本低, 仍然有很高的需求。 但是, 常规的 以 Jacobian 为基础的 IK 通常会根据实际中的限制在迭代期间将获得的接头点夹紧, 造成数字不稳定, 因为没有移动目标功能, 造成数字不稳定 。 为了缓解问题, 本研究明确考虑了联合制约因素, 特别是本文中的新 IK 解答器中的框框限制。 具体地说,, 以 校正数字回落( MDM) 为基础的反射( MDR) 方法仍然与基于 雅各布 的 IK, 所谓的 MD- IK 相容( MD- IK ) 相近于限制范围,, 一种叫做 超低调的解的解技术,, 和 Clas- clamp( ) ) 快速的解( ) 实现 快速 快速的快速的加速 方法, 最后在软件中实现一个稳定的递增到 加速 加速 。