Distance estimation from vision is fundamental for a myriad of robotic applications such as navigation, manipulation, and planning. Inspired by the mammal's visual system, which gazes at specific objects, we develop two novel constraints relating time-to-contact, acceleration, and distance that we call the $\tau$-constraint and $\Phi$-constraint. They allow an active (moving) camera to estimate depth efficiently and accurately while using only a small portion of the image. The constraints are applicable to range sensing, sensor fusion, and visual servoing. We successfully validate the proposed constraints with two experiments. The first applies both constraints in a trajectory estimation task with a monocular camera and an Inertial Measurement Unit (IMU). Our methods achieve 30-70% less average trajectory error while running 25$\times$ and 6.2$\times$ faster than the popular Visual-Inertial Odometry methods VINS-Mono and ROVIO respectively. The second experiment demonstrates that when the constraints are used for feedback with efference copies the resulting closed loop system's eigenvalues are invariant to scaling of the applied control signal. We believe these results indicate the $\tau$ and $\Phi$ constraint's potential as the basis of robust and efficient algorithms for a multitude of robotic applications.

翻译：视觉距离估计是机器人导航、操作和规划等众多应用的基础。受哺乳动物注视特定物体的视觉系统启发，我们提出了两个关于碰撞时间、加速度与距离的新型约束条件，分别称为τ约束和Φ约束。这些约束使得主动（运动）相机能够仅利用图像的一小部分即可高效而准确地估计深度。这两个约束适用于距离感知、传感器融合和视觉伺服控制。我们通过两个实验成功验证了所提出的约束条件。第一个实验在单目相机和惯性测量单元（IMU）的轨迹估计任务中同时应用了这两个约束。与流行的视觉惯性里程计方法VINS-Mono和ROVIO相比，我们的方法分别实现了平均轨迹误差降低30-70%，同时运行速度快25倍和6.2倍。第二个实验表明，当这些约束与传出副本一起用于反馈时，所得闭环系统的特征值对施加的控制信号缩放具有不变性。我们认为这些结果揭示了τ和Φ约束在众多机器人应用中作为鲁棒且高效算法基础的潜力。