This article presents a novel estimation method of the external force in linear series elastic actuators (SEAs). Conventionally, such force is estimated through the deflection of an elastic element, placed between motor and end-effector in SEAs (measured using two encoders). However, in some applications (e.g., wearable devices), it is difficult to mount a load-side encoder, due to cost or manufacturing issue. Moreover, methods based on encoders have limitations in terms of bandwidth, and, in turn, in estimating fast-varying impact forces. Additionally, SEAs may have a nonnegligible end-effector mass, therefore gravity (or accelerations of the actuator support) may add a contribution to the external force, not accounted by deflection-based estimation methods. To address these issues, we propose a method based on the Kalman filter in combination with the use of two MEMS accelerometers, mounted on the load-side and on the support of the SEA, for external force estimation and gravity (or support acceleration) compensation, respectively. We tested the proposed method even in a reduced version, with a single load-side accelerometer. Finally, it is shown that using the acceleration signal also improves the robustness against spring stiffness variations, compared to conventional methods. The experimental results show the effectiveness of the proposed methods.

中文翻译：

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无负载侧编码器的线性串联弹性执行器的外力估计

本文提出了一种新的线性串联弹性致动器 (SEA) 外力估计方法。通常，这种力是通过弹性元件的偏转来估计的，弹性元件放置在 SEA 中的电机和末端执行器之间（使用两个编码器测量）。然而，在某些应用（例如，可穿戴设备）中，由于成本或制造问题，很难安装负载侧编码器。此外，基于编码器的方法在带宽方面存在局限性，进而在估计快速变化的冲击力方面存在局限性。此外，SEA 可能具有不可忽略的末端执行器质量，因此重力（或致动器支撑的加速度）可能会增加外力的贡献，而不是基于偏转的估计方法。为了解决这些问题，我们提出了一种基于卡尔曼滤波器的方法，结合使用两个 MEMS 加速度计，安装在负载侧和 SEA 的支撑上，分别用于外力估计和重力（或支撑加速度）补偿。即使在简化版本中，我们也使用单个负载侧加速度计测试了所提出的方法。最后，结果表明，与传统方法相比，使用加速度信号还可以提高对弹簧刚度变化的鲁棒性。实验结果表明了所提出方法的有效性。带有单个负载侧加速度计。最后，结果表明，与传统方法相比，使用加速度信号还可以提高对弹簧刚度变化的鲁棒性。实验结果表明了所提出方法的有效性。带有单个负载侧加速度计。最后，结果表明，与传统方法相比，使用加速度信号还可以提高对弹簧刚度变化的鲁棒性。实验结果表明了所提出方法的有效性。