Abstract The research works carried out in this paper deal with the control of a fast double-steering off-road mobile robot. Such kind of robots requires very high stable and accurate controllers because their mobility is particularly influenced by wheel–ground interactions. Hence, the vehicle dynamics should be incorporated in the control circuit to take into account these issues, which is developed based on the road geometry parameters and the slippage-friction conditions at the wheel–ground contacts. Relying on this dynamic model, we present in this paper the design and application of a constrained Model Predictive Control (MPC). It is based on the minimization of a cost function (optimizing the deviation from the reference trajectory, and the variation of the control input) along a finite prediction horizon, however, the prediction horizon is variable according to the forward speed of the robot. On the other hand, this approach incorporates several constraints, essentially important for the stability and safety of an off-road mobile robot moving at the high velocity, namely : saturation and maximum variations of the vehicle’s actuators (i.e. steering joints and their speeds limits) as well as the tire adhesion zone bounds (allowing to validate the assumption of a linear tire model). The full optimization problem is formulated as a Linearly Constrained Quadratic Programming (QP) to compute at each time-step the optimal and dynamically-consistent front and rear steering angles that are required to reach the desired path, with respect to all these constraints. The capabilities of our proposed controller are compared with another control law which does not apply any physical or intrinsic constraints. The latter is simply a feedback controller based on the same dynamic model and LQR theory (Linear Quadratic Regulator). Both of them have been investigated through several tests on simulations via ROS/GAZEBO and experiments on a real off-road vehicle for different kinds of trajectories and velocity levels.

中文翻译：

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湿滑地面双转向漫游车动态路径跟踪的约束模型预测控制

摘要 本文的研究工作涉及快速双转向越野移动机器人的控制。这种机器人需要非常稳定和精确的控制器，因为它们的移动性特别受轮地相互作用的影响。因此，车辆动力学应纳入控制电路以考虑这些问题，这是根据道路几何参数和车轮与地面接触处的滑动摩擦条件开发的。依靠这个动态模型，我们在本文中介绍了约束模型预测控制（MPC）的设计和应用。它基于沿有限预测范围的成本函数的最小化（优化与参考轨迹的偏差和控制输入的变化），但是，预测范围根据机器人的前进速度而变化。另一方面，这种方法包含几个约束，对于高速移动的越野移动机器人的稳定性和安全性至关重要，即：车辆执行器（即转向关节及其速度限制）的饱和度和最大变化以及轮胎附着区边界（允许验证线性轮胎模型的假设）。完整的优化问题被表述为线性约束二次规划 (QP)，以在每个时间步计算到达所需路径所需的最佳且动态一致的前后转向角，相对于所有这些约束。我们提出的控制器的能力与另一个不应用任何物理或内在约束的控制法则进行了比较。后者只是一个基于相同动态模型和 LQR 理论（线性二次调节器）的反馈控制器。已经通过 ROS/GAZEBO 的多次模拟测试和针对不同轨迹和速度水平的真实越野车辆的实验对它们两者进行了研究。