A PROBABILISTIC APPROACH FOR CALCULATING REACHABILITY SET OF HYPERSONIC REENTRY
Open Access
- Author:
- Jain, Amit
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- May 30, 2019
- Committee Members:
- Puneet Singla, Thesis Advisor/Co-Advisor
- Keywords:
- Reachability sets
Hypersonic reentry
Conjugate Unscented Transform (CUT) - Abstract:
- The computation of reachability sets has garnered a lot of attention in the context of the control of autonomous systems. Whether one is planning a path for a robotic system or designing a maneuver for a spacecraft to avoid a collision with another spacecraft, the calculation of optimal or feasible trajectories is centered around the computation of reachability sets. The reachability set is defined as the collection of all states which can be traversed from any given initial conditions with the application of admissible control. The main idea of the probabilistic approach is to consider the bounded control variables as random variables and represent the reachability sets as the level sets of the state probability density function. An advantage of such an approach is that it provides not only the boundary of the reachability set but also characterizes the probability distribution of the state variables arise due to uncertainties in initial state as well as control input. The independence of control input with state variables at a given time is exploited to develop novel methods for computation of reachability sets. The reachability sets for $M$ time steps are computed through the $M$-fold convolution of state density function with control input at each time. To overcome the significant challenge of multi-dimensional convolution of the state density function, a computationally efficient approach is developed to enable onboard computation of reachability sets. In this approach, the computation of state density function due to variation in control input at each time is made tractable by computing desired order statistical moments of state density function at each time. The Conjugate Unscented Transform (CUT) algorithm is used to compute the desired order statistical moments. Finally, a prototype model of the hypersonic re-entry problem is considered to show the efficacy and utility of the proposed ideas.