# Towards a Multi-Perspective Time of Flight Laser Ranging Device Based on Mirrors and Prisms
## 1 Introduction  
In recent years, we have observed a change in the way robots are used in the industry. The workspaces of robots and humans are beginning to overlap, which is allowed by the introduction of collaborative robots that are designed so that they cannot harm humans. Inherent safety mostly stems from monitoring the forces acting on the robot and stopping the motion when the measured values exceed the calculated expected values. In addition to using robots designed not to harm humans, speed and separation monitoring (SSM) can also be used [1]. This approach is becoming increasingly common. In its simplest form, SSM is implemented using an industrial 2D lidar scanner to monitor the robot's surroundings. Further improvements can be achieved by monitoring the robot's environment with a depth camera [2, 3]. This way, it is possible to determine not only where the operator is standing, but also whether the operator is reaching in the direction of the robot, allowing for even more nuanced SSM. A problem with observing the robot's surroundings form a single field of view (FOV) is occlusions. To obtain a better representation of the robot's surroundings, multiple depth cameras, placed in different locations, can be used [4, 5]. Another approach that may be used to solve occlusion is to mount a complementary depth camera or laser time of flight (ToF) proximity sensors onto a robot [6, 7]. A similar safety system can be implemented by distributing individual proximity sensors over the robot without using an external depth camera [8, 9, 10]. To reap the full benefits of such a configuration, the position and orientation of the sensors must be considered to achieve maximum data throughput while minimizing blind spots [11], as sensors may interfere with one another'soperation when their FOVs overlap. Readings from the sensors can be used to implement a continuous SSM response-slow down or stop when an obstacle is detected-or to implement an advanced collision avoidance algorithm [12; 13]. All of the cited work using ToF proximity sensors relied on mounting them all over the robot or introduced massive dead zones around the robot where targets could not be detected. We believe that imitating the effect of distributing a plurality of individual ToF sensors across the robot is a promising approach. This could be achieved by mounting a centralized range finder with multiple FOVs on the end of the robot's segment and distributing its FOVs across the joint by the means of mirrors or prisms. The use of a centralized multi-perspective ranging device could allow us to achieve better performance or lower system cost, since some common components could be reused for all channels. The redirecting of lidar's FOV with a mirror, located within its dead zone, is a common practice in modern lidar scanners [14]. Much less research has been conducted for configurations where the redirection element may be located anywhere within the ranging device's FOV. Notable exceptions are researches where mirrors were used to expand the FOV of a scanning lidar [15; 16; 17] and the study that achieved a simulated multiple depth camera setup for 3D object capture by reflecting parts of the depth camera's FOV in [18]. The listed studies proved that mirrors can be used for redirecting light-based ToF ranging device's FOV but did not go into detail about how the mirror affects measurement characteristics. In order to pursue the direction of equipping a robot with a multi-perspective light ToF ranging device with redirected FOVs, this paper analyzes the effects of mirrors and prisms in expected real conditions at different distances from the ranging device on its ranging performance. The direct ToF measurement approach with time over threshold (TOT)-based walk error compensation was selected as it does not require a long integration time, and therefore allows a higher measurement rate and introduces only negligible motion blur [19].