We present a design method for the admittance control of a class of omnidirectional mobile platforms. Holonomic behavior of the platform is accomplished by a steering system that is itself subject to nonholonomic constraints. The proposed application of this type of platform, henceforth the “walker”, is as an assistive device for human gait rehabilitation. Therefore, the control design objectives are to guarantee the stability of the coupled system formed by the robotic platform and the human body, and to maximize mobility for the user by reducing the robot’s apparent inertia. First, we show how feedback linearization of a reduced-order model of the system, combined with a smooth trajectory-tracking control, achieves global asymptotic stability of the tracking error. Then we show how compliance in the robot limits the amount of inertia reduction that can be achieved before instability occurs. We address this problem with a control design method that maximizes the amplitude of the system’s admittance over a useful range of frequencies. Using root locus analysis and sensitivity transfer functions, we find an optimal value for the virtual mass in the admittance model, representing the best tradeoff between two oscillatory modes. The walker’s admittance vs. frequency function is then corrected via a complementary sensor input, namely, the user’s torque on the sagittal plane. A second layer of control provides the walker’s therapeutic action, consisting of a variable horizontal force that aids propulsion of the user’s body. The level of assistive force is modulated with the patient’s gait speed and turning rate to ensure easy adaptation. The control design was validated through an experiment involving human users walking in a prototype of the mobile platform.

我们提出了一种用于一类全向移动平台的导纳控制的设计方法。平台的完整性能是通过本身受非完整约束的转向系统完成的。此类平台的拟议应用（以下简称“助行器”）是用于步态康复的辅助设备。因此，控制设计目标是确保由机器人平台和人体形成的耦合系统的稳定性，并通过减少机器人的视在惯性来最大程度地提高用户的移动性。首先，我们展示了系统的降阶模型的反馈线性化与平滑的轨迹跟踪控制相结合如何实现跟踪误差的全局渐近稳定性。然后，我们展示了机器人的顺应性如何限制在不稳定发生之前可以实现的惯性减小量。我们通过一种控制设计方法解决了这个问题，该方法可以在一个有用的频率范围内最大化系统导纳的幅度。使用根轨迹分析和灵敏度传递函数，我们在导纳模型中找到虚拟质量的最佳值，代表两个振荡模式之间的最佳折衷。然后，通过互补的传感器输入（即用户在矢状面上的扭矩）校正步行者的导纳与频率的函数。第二层控制提供助行器的治疗作用，该作用由可变的水平力组成，可帮助推动使用者的身体。辅助力量的大小由患者的步态速度和转弯速度调节，以确保轻松适应。通过一项涉及人类用户在移动平台原型中行走的实验，对控件设计进行了验证。