基於無損型卡爾曼濾波器之非線性狀態估測之順應性即時步態產生器於人型機器人

Abstract

因為人型機器人的高度自由度與複雜性，在一些如非等高行走、類人型步態、外力干擾與不平整地面等變因下保持穩定行走被認為是個研究挑戰。其中，ASIMO的人型機器人，其藉由結合各種方案如著地作用力控制、線上ZMP修正、著地位置控制等控制演算法展現了良好的行走軌跡。至此，良好的行走軌跡產生器在機器人領域一直是個炙手可熱的研究議題。然而，一個軌跡產生器需要結合良好的機器人狀態估測器得知身體質心位置、速度與角動量以便於回饋使機器人穩定。 在傳統的軌跡產生器中，軌跡大多遵循著一些限制以利於數學式在物理量上的簡化如質心數量簡化、角動量忽略、質心等高、零力矩點限制、非即時運算…等。上述問題的簡化有利於線性化數學式，同時也減少狀態估測的困難性，目前常見的方法是使用卡爾曼濾波器進行即時的運算。然而，較新穎的軌跡規劃產生器並不適用於線性的卡爾曼濾波器，許多非線性的運動方程無法表示。其中，另一派學者使用擴展式卡爾曼濾波器將非線性的部分使用雅可比方程式線性化以表示其運動方程，此方法有幾個致命性的問題如: (1.)擴展式卡爾曼濾波器不是最佳化濾波器，無法表示泰勒展開式第二項以後的項目。(2.)在實際應用下，數學式的偏微分或數學式本身並不是如此容易取得，因而產生實作上的困難。 為此，本論文提出一個配合新穎且非線性的機器人狀態估測器配合新穎的軌跡產生器。就由以下流程實踐完整的控制迴路: (1.)藉由步態規劃決定基本參數。(2.)使用發散分量運動軌跡產生器實踐即時的軌跡規劃。(3.)使用最佳化分析決定身體質心高度。(4.)估測器回饋以穩定零力矩點。藉由此估測器，我們突破在即時回饋的條件下非線性問題使機器人擁有更快的行走速度與產生順應性的可能性。

Due to high degree of freedom and complexity of humanoid robots, humanoid robot walking has long been considered as a challenge to maintain steady walking un-der some changing conditions, including non-constant height walking, natural human-oid gaits, external interference and uneven ground. One famous walking bipeds is the ASIMO, which combines various schemes, such as ground reaction force control, online modification of the ZMP and foot landing position control, was capable of per-forming walking trajectories. Until now, a good walking trajectory generator has been a good topic in the field of robots. Nevertheless, a good trajectory generator needs to be combined with a humanoid robot state estimator to obtain the position, velocity and angular momentum of the robot for feedback control. In the case of traditional trajectory generator, the trajectory follows some re-strictions to facilitate the simplification of the physical quantity in the dynamic quan-tity such as the simplification of the number of centroids, ignorance of the angular momentum, constant height of mass, the limitation of zero moment point and offline generator. The simplification of the above problem not only makes it easier to linear-ize the mathematical formula, but also reduces the difficulty of state estimation. The current common approach is to use Kalman filter for online estimator. However, the novel trajectory planning generators do not apply to linear Kalman filters because many nonlinear equations of motion can not be expressed. Some of scholars use the extended Kalman filter to linearize the nonlinear part with the Jacobi equation to rep-resent the equation of motion. This method has several fatal problems such as: (1) The extended Kalman filter linearize non-linear component of the equation and ignore higher-degree Taylor polynomials., which takes advantage of the Jacobian matrix to calculate the first-order partial derivatives only. (2) In realistic applications, it is dif-ficult to get the Jacobian matrix to derive the non-linear equation. This paper proposes an original, nonlinear robot state estimator with a novel tra-jectory generator. The complete control loop is performed by the following processes: (1) Determine the basic parameters by gait planning. (2) Use the divergent component motion trajectory generator to implement real-time trajectory planning. (3) Use the optimization analysis to determine body mass center height. (4.) Obtain the state with estimator to stabilize zero moment points. With this estimator, we break through the non-linear problem in real-time feedback conditions to give the robot the possibility of faster walking and compliance.