To enhance accuracy of robot state estimation, active sensing (or perception-aware) methods seek trajectories that maximize the information gathered by the sensors. To this aim, one possibility is to seek trajectories that minimize the (estimation error) covariance matrix output by an extended Kalman filter (EKF), w.r.t. its control inputs over a given horizon. However, this is computationally demanding. In this article, we derive novel backpropagation analytical formulas for the derivatives of the covariance matrices of an EKF w.r.t. all its inputs. We then leverage the obtained analytical gradients as an enabling technology to derive perception-aware optimal motion plans. Simulations validate the approach, showcasing improvements in execution time, notably over PyTorch's automatic differentiation. Experimental results on a real vehicle also support the method.

翻译：为提升机器人状态估计精度，主动感知（或感知感知）方法通过优化轨迹最大化传感器采集的信息。为此，一种可行方案是寻求使扩展卡尔曼滤波（EKF）输出的（估计误差）协方差矩阵在给定预测时域内相对于其控制输入最小化的轨迹。然而，这带来了巨大的计算负担。本文推导了EKF协方差矩阵关于所有输入的导数的新型反向传播解析公式，并将所得解析梯度作为核心技术用于生成感知感知最优运动规划。仿真验证了该方法，表明其在执行时间上相较于PyTorch自动微分具有显著优势。真实车辆上的实验结果也支持了该方法的有效性。