The article proposes a nonlinear optimal (H-infinity) control approach for the model of a tracked robotic vehicle. The kinematic model of such a tracked vehicle takes into account slippage effects due to the contact of the tracks with the ground. To solve the related control problem, the dynamic model of the vehicle undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the vehicle. For the approximately linearized description of the tracked vehicle a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control, that is fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

本文提出了一种针对履带机器人车辆模型的非线性最优（H-infinity）控制方法。这种履带车辆的运动学模型考虑了由于履带与地面的接触而产生的滑移效应。为了解决相关的控制问题，车辆的动力学模型在临时操作点附近进行第一近似线性化，该线性化在控制算法的每次迭代时更新。线性化过程依赖于一阶泰勒级数展开和车辆状态空间模型的雅可比矩阵的计算。为了对被跟踪车辆进行近似线性化描述，设计了稳定的H-∞反馈控制器。为了计算控制器的反馈增益，在控制方法的每个时间步都求解了代数Riccati方程。通过Lyapunov分析证明了该控制方案的稳定性。还证明了该控制方法保留了线性最优控制的优点，即在控制输入适度变化的情况下快速准确地跟踪参考设定值。