This paper presents a formal definition and explicit representation of robot motion risk. Currently, robot motion risk has not been formally defined, but has already been used in motion and path planning. Risk is either implicitly represented as model uncertainty using probabilistic approaches, where the definition of risk is somewhat avoided, or explicitly modeled as a simple function of states, without a formal definition. In this work, we provide formal reasoning behind what risk is for robot motion and propose a formal definition of risk in terms of a sequence of motion, namely path. Mathematical approaches to represent motion risk are also presented, which is in accordance with our risk definition and properties. The definition and representation of risk provide a meaningful way to evaluate or construct robot motion or path plans. The understanding of risk is even of greater interest for the search and rescue community: the deconstructed environments cast extra risk onto the robot, since they are working under extreme conditions. A proper risk representation has the potential to reduce robot failure in the field.
Although researchers have investigated risk-aware planning from a variety of directions, including Partially Observable Markov Decision Process (POMDP) with negative reward as risk penalty @cite_5 , constrained POMDP @cite_8 , or risk allocation @cite_4 , the definition of risk was always taken for granted and only based on the ad hoc applications.
@cite_5 @cite_4 @cite_8
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Recent advances in Autonomous Underwater Vehicle (AUV) technology have facilitated the collection of oceanographic data at a fraction of the cost of ship-based sampling methods. Unlike oceanographic data collection in the deep ocean, operation of AUVs in coastal regions exposes them to the risk of collision with ships and land. Such concerns are particularly prominent for slow-moving AUVs since ocean current magnitudes are often strong enough to alter the planned path significantly. Prior work using predictive ocean currents relies upon deterministic outcomes, which do not account for the uncertainty in the ocean current predictions themselves. To improve the safety and reliability of AUV operation in coastal regions, we introduce two stochastic planners: (a) a Minimum Expected Risk planner and (b) a risk-aware Markov Decision Process, both of which have the ability to utilize ocean current predictions probabilistically. We report results from extensive simulation studies in realistic ocean current fields obtained from widely used regional ocean models. Our simulations show that the proposed planners have lower collision risk than state-of-the-art methods. We present additional results from field experiments where ocean current predictions were used to plan the paths of two Slocum gliders. Field trials indicate the practical usefulness of our techniques over long-term deployments, showing them to be ideal for AUV operations. This paper proposes a novel two-stage optimization method for robust model predictive control (RMPC) with Gaussian disturbance and state estimation error. Since the disturbance is unbounded, it is impossible to achieve zero probability of violating constraints. Our goal is to optimize the expected value of an objective function while limiting the probability of violating any constraints over the planning horizon (joint chance constraint). Prior arts include ellipsoidal relaxation approach [1] and particle control [2], but the former yields very conservative result and the latter is computationally intensive. Our approach divide the optimization problem into two stages; the upper-stage that optimizes risk allocation, and the lower-stage that optimizes control sequence with tightened constraints. The lower-stage is a regular convex optimization, such as linear programming or quadratic programming. The upper-stage is also convex, but the objective function is not always differentiable. We developed a fast descent algorithm for the upper-stage called iterative risk allocation (IRA), which yield much smaller suboptimality than ellipsoidal relaxation method while achieving a substantial speedup compared to and particle control. This work seeks to address the problem of planning in the presence of uncertainty and constraints. Such problems arise in many situations, including the basis of this work, which involves planning for a team of first responders (both humans and robots) operating in an urban environment. The problem is framed as a Partially-Observable Markov Decision Process (POMDP) with constraints, and it is shown that even in a relatively simple planning problem, modeling constraints as large penalties does not lead to good solutions. The main contribution of the work is a new online algorithm that explicitly ensures constraint feasibility while remaining computationally tractable. Its performance is demonstrated on an example problem and it is demonstrated that our online algorithm generates policies comparable to an offline constrained POMDP algorithm.