A nonparametric adaptive controller is proposed for crane control where the payload tracks a desired trajectory with feedback from the payload position. The controller is based on a novel version of partial feedback linearization where the unactuated crane load dynamics are controlled with the position of the actuated crane dynamics instead of the acceleration. This is made possible by taking advantage of the gravity terms in a new Cartesian model that we propose for the load dynamics. This Cartesian model structure makes it possible to implement a nonparametric adaptive controller which cancels disturbances on the crane load by approximating the effects of unknown disturbance forces and structurally unknown dynamics in a reproducing kernel Hilbert space (RKHS). It is shown that the nonparametric adaptive controller leads to uniformly ultimately bounded errors in the presence of unknown forces and unmodeled dynamics. In addition, it is shown that the proposed partial feedback linearization based on the Cartesian model has certain advantages in payload tracking control also in the non-adaptive case. The performance of the nonparametric adaptive controller is validated in simulation and experiments with good results.

翻译：本文提出了一种用于起重机控制的非参数自适应控制器，其中有效载荷根据其位置反馈跟踪期望轨迹。该控制器基于一种新颖的部分反馈线性化方法，其中未受驱动的起重机负载动力学通过受驱动的起重机动力学位置而非加速度进行控制。这一方法得以实现，得益于我们为负载动力学提出的新型笛卡尔模型中重力项的利用。该笛卡尔模型结构使得非参数自适应控制器的实现成为可能，通过在再生核希尔伯特空间（RKHS）中近似未知扰动力和结构未知动力学的影响，从而抵消起重机负载上的扰动。研究表明，在存在未知力和未建模动力学的情况下，该非参数自适应控制器能实现一致最终有界误差。此外，基于笛卡尔模型提出的部分反馈线性化在非自适应情况下对有效载荷跟踪控制也具有特定优势。通过仿真和实验验证了非参数自适应控制器的性能，并取得了良好结果。