Spacecraft Motion Planning and Control under Probabilistic Uncertainty for Coordinated Inspection and Safe Learning

Citation

Nakka, Yashwanth Kumar (2021) Spacecraft Motion Planning and Control under Probabilistic Uncertainty for Coordinated Inspection and Safe Learning. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6329-sf68. https://resolver.caltech.edu/CaltechTHESIS:05142021-163257155

Abstract

During a spacecraft mission design process, engineers often balance the following three criteria: science return, optimality in performance, and safety. Given a science criterion, engineers design the orbit parameters with predefined performance and safety. Often in this approach, the spacecraft has no understanding of the expected outcome or the knowledge of the mission safety criteria. Autonomous science-driven orbit (or goal) selection and planning for safety under uncertainty enable efficient and adaptable missions. To this end, we propose an architecture for information-based guidance and control for coordinated inspection, motion planning and control algorithms for safe and optimal guidance under uncertainty, and architecture for safe exploration.

In the first part of this thesis, we present an architecture for inspection or mapping of a target spacecraft in a low Earth orbit using multiple observer spacecraft. We use an information gain approach to directly consider the trade-off between gathered data and fuel/energy cost. The estimated information gain is a crucial input to the motion planner, which computes orbits and reconfiguration strategies for each of the observers to maximize the information gain from distributed observations of the target spacecraft. The resulting motion trajectories jointly consider observational coverage of the target spacecraft and fuel/energy cost. We validate our architecture in a mission simulation to visually inspect the target spacecraft and on the three degree-of-freedom robotic spacecraft dynamics simulator testbed.

In the second part of the thesis, we present gPC-SCP, Generalized Polynomial Chaos-based Sequential Convex Programming method, to compute a sub-optimal solution for a continuous-time chance-constrained stochastic nonlinear optimal control (SNOC) problem. The approach enables motion planning and control of robotic systems under uncertainty. The proposed method involves two steps. The first step is to derive a deterministic nonlinear optimal control problem (DNOC) with convex constraints that are surrogate to the SNOC by using gPC expansion and the distributionally-robust convex subset of the chance constraints. The second step is to solve the DNOC problem using sequential convex programming (SCP) for trajectory generation and control. We prove that in the unconstrained case, the optimal value of the DNOC converges to that of SNOC asymptotically and that any feasible solution of the constrained DNOC is a feasible solution of the chance-constrained SNOC. We derive a stable stochastic model predictive controller using the gPC-SCP for tracking a potentially unsafe trajectory in the presence of uncertainty. We empirically demonstrate the efficacy of the gPC-SCP method for the following three test cases: 1) collision checking under uncertainty in actuation, 2) collision checking with stochastic obstacles, and 3) safe trajectory tracking under uncertainty in the dynamics and obstacle location by using a receding horizon control approach. We validate the effectiveness of the gPC-SCP method on the robotic spacecraft testbed.

In the third part of this thesis, we present a new approach for optimal motion planning for safe exploration that integrates the chance-constrained stochastic optimal control with dynamics learning and feedback control. We derive an iterative convex optimization algorithm that solves an Information-cost Stochastic Nonlinear Optimal Control problem (Info-SNOC). The optimization objective encodes control cost for performance and exploration cost for learning, and the safety is incorporated as distributionally robust chance constraints. The dynamics are predicted from a robust regression model that is learned from data. The Info-SNOC algorithm is used to compute a sub-optimal pool of safe motion plans that aid in exploration for learning unknown residual dynamics under safety constraints. A stable feedback controller is used to execute the motion plan and collect data for model learning. We prove the safety of rollout from our exploration method and reduction in uncertainty over epochs, thereby guaranteeing the consistency of our learning method. We validate the effectiveness of Info-SNOC by designing and implementing a pool of safe trajectories for a planar robot. We demonstrate that our approach has a higher success rate in ensuring safety when compared to a deterministic trajectory optimization approach.

Thesis Files