Mixed-Strategy Chance Constrained Optimal Control

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Joint Chance-Constrained Dynamic Programming

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Joint Chance-Constrained Dynamic Programming

This paper presents a novel dynamic programming algorithm with a joint chance constraint, which explicitly bounds the risk of failure in order to maintain the state within a specified feasible region. A joint chance constraint cannot be handled by existing constrained dynamic programming approaches since their application is limited to constraints in the same form as the cost function, that is, an expectation over a sum of one-stage costs. We overcome this challenge by reformulating the joint chance constraint into a constraint on an expectation over a sum of indicator functions, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the primal variables can be optimized by a standard dynamic programming, while the dual variable is optimized by a root-finding algorithm that converges exponentially. Error bounds on the primal and dual objective values are rigorously derived. We demonstrate the algorithm on a path planning problem, as well as an optimal control problem for Mars entry, descent and landing. The simulations are conducted using a real terrain data of Mars, with four million discrete states at each time step

A Risk-Constrained Multi-Stage Decision Making Approach to the Architectural Analysis of Mars Missions

This paper presents a novel risk-constrained multi-stage decision making approach to the architectural analysis of planetary rover missions. In particular, focusing on a 2018 Mars rover concept, which was considered as part of a potential Mars Sample Return campaign, we model the entry, descent, and landing (EDL) phase and the rover traverse phase as four sequential decision-making stages. The problem is to find a sequence of divert and driving maneuvers so that the rover drive is minimized and the probability of a mission failure (e.g., due to a failed landing) is below a user specified bound. By solving this problem for several different values of the model parameters (e.g., divert authority), this approach enables rigorous, accurate and systematic trade-offs for the EDL system vs. the mobility system, and, more in general, cross-domain trade-offs for the different phases of a space mission. The overall optimization problem can be seen as a chance-constrained dynamic programming problem, with the additional complexity that 1) in some stages the disturbances do not have any probabilistic characterization, and 2) the state space is extremely large (i.e, hundreds of millions of states for trade-offs with high-resolution Martian maps). To this purpose, we solve the problem by performing an unconventional combination of average and minimax cost analysis and by leveraging high efficient computation tools from the image processing community. Preliminary trade-off results are presented

Enhanced Mars Rover Navigation Techniques

Robust navigation through rocky terrain by small mobile robots is important for maximizing science return from upcoming missions to Mars. We are addressing this problem at multiple levels through the development of intelligent se- quencing, sensor constrained path planning, natural terrain visual localization, and real. time state estimation. Each of these techniques will be described, and their complementary aspects discussed. Experimental results are provided from implementation on our Mars rover prototype operating in realistic scenarios

A Prototype Manipulation System for Mars Rover Science Operations

This paper provides an overview of a new manipulation system developed for sampling and instrument placement from small autonomous mobile robots for Mars exploration. Selected out of the design space, two manipulators have been constructed and integrated into the Rocky 7 Mars rover prototype 1 . This paper describes the design objectives and constraints for these manipulators, and presents the finished system and some results from its operation. 1 Introduction In 1996, NASA launched the first of a series of spacecraft to revisit the planet Mars. This Pathfinder 2 lander contains the mobile robot, Sojourner, a 12 kg six-wheeled mobile robot which will venture out from the lander, taking pictures and positioning a science instrument against designated soil and rocks. Subsequent to this mission, there are plans to return to the surface of Mars every 26 months through 2005. Based on previous rover prototypes [3], Sojourner is designed to demonstrate the viability of mobile robot explo..