Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect

SPECT Imaging Agents for Detecting Cerebral β-Amyloid Plaques

The development of radiotracers for use in vivo to image β-amyloid (Aβ) plaques in cases of Alzheimer's disease (AD) is an important, active area of research. The presence of Aβ aggregates in the brain is generally accepted as a hallmark of AD. Since the only definitive diagnosis of AD is by postmortem staining of affected brain tissue, the development of techniques which enable one to image Aβ plaques in vivo has been strongly desired. Furthermore, the quantitative evaluation of Aβ plaques in the brain could facilitate evaluation of the efficacy of antiamyloid therapies currently under development. This paper reviews the current situation in the development of agents for SPECT-based imaging of Aβ plaques in Alzheimer's brains

Two-stage Optimization Approach to Robust Model Predictive Control with a Joint Chance Constraint

When controlling dynamic systems such as mobile robots in uncertain environments, there is a trade off between risk and reward. For example, a race car can turn a corner faster by taking a more challenging path. This paper proposes a new approach to planning a control sequence with guaranteed risk bound. Given a stochastic dynamic model, the problem is to find a control sequence that optimizes a performance metric, while satisfying chance constraints i.e. constraints on the upper bound of the probability of failure. We propose a two-stage optimization approach, with the upper stage optimizing the risk allocation and the lower stage calculating the optimal control sequence that maximizes the reward. In general, upper-stage is a non-convex optimization problem, which is hard to solve. We develop a new iterative algorithm for this stage that efficiently computes the risk allocation with a small penalty to optimality. The algorithm is implemented and tested on the autonomous underwater vehicle (AUV) depth planning problem, which demonstrates the substantial improvement in computation cost and suboptimality compared to the prior arts

Risk Allocation for Multi-agent Systems using Tatonnement

This paper proposes a new market-based distributed planning algorithm for multi-agent systems under uncertainty, called MIRA (Market-based Iterative Risk Allocation). In large coordination problems, from power grid management to multi-vehicle missions, multiple agents act collectively in order to optimize the performance of the system, while satisfying mission constraints. These optimal plans are particularly susceptible to risk when uncertainty is introduced. We present a distributed planning algorithm that minimizes the system cost while ensuring that the probability of violating mission constraints is below a user-specified level. We build upon the paradigm of risk allocation (Ono and Williams, AAAI-08), in which the planner optimizes not only the sequence of actions, but also its allocation of risk among each constraint at each time step. We extend the concept of risk allocation to multi-agent systems by highlighting risk as a good that is traded in a computational market. The equilibrium price of risk that balances the supply and demand is found by an iterative price adjustment process called tatonnement (also known as Walrasian auction). The simulation results demonstrate the efficiency and optimality of the proposed distributed planner.This research is funded by The Boeing Company grant MIT-BA-GTA-1

Efficient Motion Planning Algorithm for Stochastic Dynamic Systems with Constraints on Probability of Failure

When controlling dynamic systems such as mobile robots in uncertain environments, there is a trade off between risk and reward. For example, a race car can turn a corner faster by taking a more challenging path. This paper proposes a new approach to planning a control sequence with guaranteed risk bound. Given a stochastic dynamic model, the problem is to find a control sequence that optimizes a performance metric, while satisfying chance constraints i.e. constraints on the upper bound of the probability of failure. We propose a two-stage optimization approach, with the upper stage optimizing the risk allocation and the lower stage calculating the optimal control sequence that maximizes the reward. In general, upper-stage is a non-convex optimization problem, which is hard to solve. We develop a new iterative algorithm for this stage that efficiently computes the risk allocation with a small penalty to optimality. The algorithm is implemented and tested on the autonomous underwater vehicle (AUV) depth planning problem, which demonstrates the substantial improvement in computation cost and suboptimality compared to the prior arts

Market-based Risk Allocation for Multi-agent Systems

This paper proposes Market-based Iterative Risk Allocation (MIRA), a new market-based distributed planning algorithm for multi-agent systems under uncertainty. In large coordination problems, from power grid management to multi-vehicle missions, multiple agents act collectively in order to optimize the performance of the system, while satisfying mission constraints. These optimal plans are particularly susceptible to risk when uncertainty is introduced. We present a distributed planning algorithm that minimizes the system cost while ensuring that the probability of violating mission constraints is below a user-specified level. We build upon the paradigm of risk allocation (Ono & Williams 2008), in which the planner optimizes not only the sequence of actions, but also its allocation of risk among each constraint at each time step. We extend the concept of risk allocation to multi-agent systems by highlighting risk as a commodity that is traded in a computational market. The equilibrium price of risk that balances the supply and demand is found by an iterative price adjustment process called tˆatonnement (also known as Walrasian auction). Our work is distinct from the classical tˆatonnement approach in that we use Brent’s method to provide fast guaranteed convergence to the equilibrium price. The simulation results demonstrate the efficiency of the proposed distributed planner

Risk-Constrained Dynamic Programming for Optimal Mars Entry, Descent, and Landing

A chance-constrained dynamic programming algorithm was developed that is capable of making optimal sequential decisions within a user-specified risk bound. This work handles stochastic uncertainties over multiple stages in the CEMAT (Combined EDL-Mobility Analyses Tool) framework. It was demonstrated by a simulation of Mars entry, descent, and landing (EDL) using real landscape data obtained from the Mars Reconnaissance Orbiter. Although standard dynamic programming (DP) provides a general framework for optimal sequential decisionmaking under uncertainty, it typically achieves risk aversion by imposing an arbitrary penalty on failure states. Such a penalty-based approach cannot explicitly bound the probability of mission failure. A key idea behind the new approach is called risk allocation, which decomposes a joint chance constraint into a set of individual chance constraints and distributes risk over them. The joint chance constraint was reformulated into a constraint on an expectation over a sum of an indicator function, which can be incorporated into the cost function by dualizing the optimization problem. As a result, the chance-constraint optimization problem can be turned into an unconstrained optimization over a Lagrangian, which can be solved efficiently using a standard DP approach