This paper develops a path planner that minimizes risk (e.g. motion execution) while maximizing accumulated reward (e.g., quality of sensor viewpoint) motivated by visual assistance or tracking scenarios in unstructured or confined environments. In these scenarios, the robot should maintain the best viewpoint as it moves to the goal. However, in unstructured or confined environments, some paths may increase the risk of collision; therefore there is a tradeoff between risk and reward. Conventional state-dependent risk or probabilistic uncertainty modeling do not consider path-level risk or is difficult to acquire. This risk-reward planner explicitly represents risk as a function of motion plans, i.e., paths. Without manual assignment of the negative impact to the planner caused by risk, this planner takes in a pre-established viewpoint quality map and plans target location and path leading to it simultaneously, in order to maximize overall reward along the entire path while minimizing risk. Exact and approximate algorithms are presented, whose solution is further demonstrated on a physical tethered aerial vehicle. Other than the visual assistance problem, the proposed framework also provides a new planning paradigm to address minimum-risk planning under dynamical risk and absence of substructure optimality and to balance the trade-off between reward and risk.
The trade-off between reward and risk was mostly addressed as chance or probability of success failure. @cite_12 @cite_2 proposed chance-constrained rapidly-exploring random tree (CC-RRT) approaches, which used chance constraints to guarantee probabilistic feasibility at each time step and over entire trajectory. Another popular approach to handle reward and risk is to use (PO)MDP. As standard MDP inherently contains reward but not risk, researchers have looked into representing risk as negative reward (penalty) @cite_21 or constraints (C-POMDP) with unit cost for constraint violation @cite_11 @cite_23 @cite_25 . Going beyond unit cost, CC-POMDP was proposed by @cite_1 , which was based on a bound on the probability (chance) of some event happening during policy execution. RMPC is another alternative, with an emphasis on risk allocation, i.e., to allocate more risk for more rewarding actions @cite_7 @cite_13 .
@cite_7 @cite_21 @cite_1 @cite_23 @cite_2 @cite_13 @cite_25 @cite_12 @cite_11
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Autonomous agents operating in partially observable stochastic environments often face the problem of optimizing expected performance while bounding the risk of violating safety constraints. Such problems can be modeled as chance-constrained POMDP's (CC-POMDP's). Our first contribution is a systematic derivation of execution risk in POMDP domains, which improves upon how chance constraints are handled in the constrained POMDP literature. Second, we present RAO*, a heuristic forward search algorithm producing optimal, deterministic, finite-horizon policies for CC-POMDP's. In addition to the utility heuristic, RAO* leverages an admissible execution risk heuristic to quickly detect and prune overly-risky policy branches. Third, we demonstrate the usefulness of RAO* in two challenging domains of practical interest: power supply restoration and autonomous science agents. between planner conservatism and the risk of infeasibility. This paper presents a novel real-time planning algorithm, chance constrained rapidly-exploring random trees (CC-RRT), which uses chance constraints to guarantee probabilistic feasibility for linear systems subject to process noise and or uncertain, possibly dynamic obstacles. By using RRT, the algorithm enjoys the computational benets of sampling-based algorithms, such as trajectory-wise constraint checking and incorporation of heuristics, while explicitly incorporating uncertainty within the formulation. Under the assumption of Gaussian noise, probabilistic feasibility at each time step can be established through simple simulation of the state conditional mean and the evaluation of linear constraints. Alternatively, a small amount of additional computation can be used to explicitly compute a less conservative probability bound at each time step. Simulation results show that this algorithm can be used for ecient identication and execution of probabilistically safe paths in real time. We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng (1999), but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method applies to arbitrary POMDPs, including ones with infinite state and action spaces. We also present empirical results for our approach on a small discrete problem, and on a complex continuous state continuous action problem involving learning to ride a bicycle. The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.