Robust Proximity Operations using Probabilistic Markov Models

TL;DR

A Markov decision process-based state switching is devised, implemented, and analyzed for proximity operations of various autonomous vehicles to enable robust and efficient proximity operations.

Abstract

A Markov decision process-based state switching is devised, implemented, and analyzed for proximity operations of various autonomous vehicles. The framework contains a pose estimator along with a multi-state guidance algorithm. The unified pose estimator leverages the extended Kalman filter for the fusion of measurements from rate gyroscopes, monocular vision, and ultra-wideband radar sensors. It is also equipped with Mahalonobis distance-based outlier rejection and under-weighting of measurements for robust performance. The use of probabilistic Markov models to transition between various guidance modes is proposed to enable robust and efficient proximity operations. Finally, the framework is validated through an experimental analysis of the docking of two small satellites and the precision landing of an aerial vehicle.

Figures (10)

• Figure 1: Three stage guidance algorithm for TPODS docking : The initial motion is in the direction of the target, followed by a reorientation to the desired docking attitude. Finally, the chaser aligns directly in front of the docking face and completes the docking. Availability of vision measurements is depicted with a change in the color of the camera FOV cone.
• Figure 2: TPODS module uses UWB radar in two-way ranging mode to measure the distance to stationary anchors. Since the anchors and UWB sensor are not mounted at respective centers of mass, rotational and translation motion of the UWB sensor relative to the stationary anchors are coupled.
• Figure 3: Simulation setup : The true states consist of relative position and velocity (expressed in reference frame $\boldsymbol{\hat{c}}$), attitude quaternion, and angular velocities (expressed in reference frame $\boldsymbol{\hat{d}}$). Generated measurements are relative range to a specific anchor, angular velocities, and location of feature points if the target is within camera FOV.
• Figure 4: State machine for docking guidance along with respective transition probabilities. Since each $A_{ij}$ represents a probability, they have to be non-dimensional and their magnitude must lie between 0 and 1. In addition, the total probability of all outgoing arrows from a state must add to 1.
• Figure 5: Comparison of trajectories with fixed and adaptive switching distances for 500 run Monte-Carlo simulation. The target is located at $(1,2,1)m$ having the orientation $\left(\theta_x,\theta_y,\theta_z\right)=\left(-90\degree,0\degree,-90\degree\right)$, while the chaser is located at $(0,1,0)m$ with the orientation $\left(0\degree,0\degree,0\degree\right)$. The camera sensor is mounted at the bottom face of the chaser.