Suman Chakravorty

FIRM: Sampling-based feedback motion-planning under motion uncertainty and imperfect measurements

In this paper we present feedback-based information roadmap (FIRM), a multi-query approach for planning under uncertainty which is a belief-space variant of probabilistic roadmap methods. The crucial feature of FIRM is that the costs associated with the edges are independent of each other, and in this sense it is the first method that generates a graph in belief space that preserves the optimal substructure property. From a practical point of view, FIRM is a robust and reliable planning framework. It is robust since the solution is a feedback and there is no need for expensive replanning. It is reliable because accurate collision probabilities can be computed along the edges. In addition, FIRM is a scalable framework, where the complexity of planning with FIRM is a constant multiplier of the complexity of planning with PRM. In this paper, FIRM is introduced as an abstract framework. As a concrete instantiation of FIRM, we adopt stationary linear quadratic Gaussian (SLQG) controllers as belief stabilizers and introduce the so-called SLQG-FIRM. In SLQG-FIRM we focus on kinematic systems and then extend to dynamical systems by sampling in the equilibrium space. We investigate the performance of SLQG-FIRM in different scenarios.

Generalized Sampling-Based Motion Planners

In this paper, generalized versions of the probabilistic sampling-based planners, i.e., probabilistic roadmaps and rapidly exploring random tree, are presented. The generalized planners, i.e., generalized probabilistic roadmap and the generalized rapidly exploring random tree, result in hybrid hierarchical feedback planners that are robust to the uncertainties in the robot motion model and in the robot map or workspace. The proposed planners are analyzed and shown to probabilistically be complete. The algorithms are tested on fully actuated and underactuated robots on several maps of varying degrees of difficulty, and the results show that the generalized methods have a significant advantage over the traditional methods when planning under uncertainty.

FIRM: Feedback controller-based information-state roadmap - A framework for motion planning under uncertainty

Direct transformation of sampling-based motion planning methods to the Information-state (belief) space is a challenge. The main bottleneck for roadmap-based techniques in belief space is that the incurred costs on different edges of the graph are not independent of each other. In this paper, we generalize the Probabilistic RoadMap (PRM) framework to obtain a Feedback controller-based Information-state RoadMap (FIRM) that takes into account motion and sensing uncertainty in planning. The FIRM nodes and edges lie in belief space and the crucial feature of FIRM is that the costs associated with different edges of FIRM are independent of each other. Therefore, this construct essentially breaks the “curse of history” in the original Partially Observable Markov Decision Process (POMDP), which models the planning problem. Further, we show how obstacles can be rigorously incorporated into planning on FIRM. All these properties stem from utilizing feedback controllers in the construction of FIRM.

The Partition of Unity Finite Element Approach to the Stationary Fokker-Planck Equation

The stationary Fokker-Planck Equation (FPE) is solved for nonlinear dynamic systems using a local numerical technique based on the meshless Partition of Unity Finite Element Method (PUFEM). The method is applied to the FPE for two-dimensional dynamical systems, and argued to be an excellent candidate for higher dimensional systems and the transient problem. Variations of the conventional PUFEM are used to improve the quality of approximation, by using novel pasting functions to blend the various local approximations. These functions, besides satisfying the conditions for a partition of unity are easy to integrate numerically and provide solution continuity of any desired order. Results are compared with existing global and local techniques.

Robust online belief space planning in changing environments: Application to physical mobile robots

Motion planning in belief space (under motion and sensing uncertainty) is a challenging problem due to the computational intractability of its exact solution. The Feedback-based Information RoadMap (FIRM) framework made an important theoretical step toward enabling roadmap-based planning in belief space and provided a computationally tractable version of belief space planning. However, there are still challenges in applying belief space planners to physical systems, such as the discrepancy between computational models and real physical models. In this paper, we propose a dynamic replanning scheme in belief space to address such challenges. Moreover, we present techniques to cope with changes in the environment (e.g., changes in the obstacle map), as well as unforeseen large deviations in the robots location (e.g., the kidnapped robot problem). We then utilize these techniques to implement the first online replanning scheme in belief space on a physical mobile robot that is robust to changes in the environment and large disturbances. This method demonstrates that belief space planning is a practical tool for robot motion planning.

Information space receding horizon control

In this paper, we present a receding horizon solution to the problem of optimal sensor scheduling problem. The optimal sensor scheduling problem can be posed as a Partially Observed Markov Decision Process (POMDP) whose solution is given by an Information Space (I-space) Dynamic Programming (DP) problem. We present a simulation based stochastic optimization technique that, combined with a receding horizon approach, obviates the need to solve the computationally intractable I-space DP problem. The technique is tested on a simple sensor scheduling problem where a sensor has to choose among the measurements of N dynamical systems such that the information regarding the aggregate system is maximized over an infinite horizon.

Fuel Optimal Maneuvers for Multispacecraft Interferometric Imaging Systems

In this paper, the design of minimum-fuel maneuvers for multispacecraft interferometric imaging systems is studied. It is argued that the underlying optimization problem is computationally intractable, through its similarity to the traveling salesman problem, and through an optimal control argument, and thus it is necessary to resort to heuristics in order to solve the problem. The design of minimum-fuel spiral maneuvers is considered in defining the constraints on the coverage of the u-v plane. It is shown that the geometric design problem, the optimization problem obtained by fixing the angular rate of the spiral, and the kinematic design problem, obtained by fixing the spiraling rate of the spiral, are both convex in deep space, that is, perturbation free motion, and in near-Earth orbits. As an application of the methodology developed, fuel optimal maneuvers are found for a deep space imaging application and the fuel consumption and power requirements of the system are calculated to gain knowledge about the feasibility of such maneuvers.

On the probabilistic completeness of the sampling-based feedback motion planners in belief space

This paper extends the concept of “probabilistic completeness” defined for motion planners in state space (or configuration space) to the concept of “probabilistic completeness under uncertainty” for motion planners in belief space. Accordingly, an approach is proposed to verify the probabilistic completeness of the sampling-based planners in belief space. Finally, through the proposed approach, it is shown that under mild conditions the sampling-based methods constructed based on the abstract framework of FIRM (Feedback-based Information Roadmap Method) are probabilistically complete under uncertainty.

Information Space Receding Horizon Control

In this paper, we present a receding horizon solution to the optimal sensor scheduling problem. The optimal sensor scheduling problem can be posed as a partially observed Markov decision problem whose solution is given by an information space (I-space) dynamic programming (DP) problem. We present a simulation-based stochastic optimization technique that, combined with a receding horizon approach, obviates the need to solve the computationally intractable I-space DP problem. The technique is tested on a sensor scheduling problem, in which a sensor must choose among the measurements of N dynamical systems in a manner that maximizes information regarding the aggregate system over an infinite horizon. While simple, such problems nonetheless lead to very high dimensional DP problems to which the receding horizon approach is well suited.

Generalized sampling based motion planners with application to nonholonomic systems

In this paper, generalized versions of the probabilistic sampling based planners, Probabilisitic Road Maps (PRM) and Rapidly exploring Random Tree (RRT), are presented. The generalized planners, Generalized Proababilistic Road Map (GPRM) and the Generalized Rapidly Exploring Random Tree (GRRT), are designed to account for uncertainties in the robot motion model as well as uncertainties in the robot map/ workspace. The proposed planners are analyzed and shown to be probabilistically complete. The algorithms are tested by solving the motion planning problem of a nonholonomic unicycle robot in several maps of varying degrees of difficulty and results show that the generalized methods have excellent performance in such situations.