Making Adaptive an Interval Constraint Propagation Algorithm Exploiting Monotonicity

International audienceA new interval constraint propagation algorithm, called MOnotonic Hull Consistency (Mohc), has recently been proposed. Mohc exploits monotonicity of functions to better filter variable domains. Embedded in an interval-based solver, Mohc shows very high performance for solving systems of numerical constraints (equations or inequalities) over the reals. However, the main drawback is that its revise procedure depends on two user-defined parameters. This paper reports a rigourous empirical study resulting in a variant of Mohc that avoids a manual tuning of the parameters. In particular, we propose a policy to adjust in an auto-adaptive way, during the search, the parameter sensitive to the monotonicity of the revised function

Distributed Interval Synchronization

In this paper we address the problem of using pairwise measures associated with the edges of a graph to obtain absolute consistent measures associated with the nodes. This problem is known in the literature as graph synchronisation. In particular, we rigorously deal with the uncertainty affecting the measures thanks to the interval analysis approach. We propose an asynchronous, distributed algorithm that converges to an interval solution that represents all possible sharp solutions consistent with the measures

Exploitation de la monotonie des fonctions dans la propagation de contraintes sur intervalles

National audienceWe propose a new interval constraint propagation algorithm, called MOnotonic Hull Consistency (Mohc), that exploits monotonicity of functions. The propagation is standard, but the Mohc-Revise procedure, used to filter/contract the variable domains w.r.t. an individual constraint, uses monotonic versions of the classical HC4- Revise and BoxNarrow procedures. Mohc-Revise appears to be the first adaptive revise procedure ever proposed in constraint programming. Also, when a function is monotonic w.r.t. every variable, Mohc-Revise is proven to compute the optimal/ sharpest box enclosing all the solutions of the corresponding constraint (hull consistency). Very promising experimental results suggest that Mohc has the potential to become an alternative to the state-of-the-art HC4 and Box algorithms

Singularity Maps of Space Robots and their Application to Gradient-based Trajectory Planning

We present a numerical method to compute singularity sets in the configuration space of free-floating robots, comparing two different criteria based on formal methods. By exploiting specific properties of free-floating systems and an alternative formulation of the generalized Jacobian, the search space and computational complexity of the algorithm is reduced. It is shown that the resulting singularity maps can be applied in the context of trajectory planning to guarantee feasibility with respect to singularity avoidance. The proposed approach is validated on a space robot composed of a six degrees-of-freedom (DOF) arm mounted on a body with six DOF

Efficient Set-Based Approaches for the Reliable Computation of Robot Capabilities

To reliably model real robot characteristics, interval linear systems of equations allow to describe families of problems that consider sets of values. This allows to easily account for typical complexities such as sets of joint states and design parameter uncertainties. Inner approximations of the solutions to the interval linear systems can be used to describe the common capabilities of a robotic manipulator corresponding to the considered sets of values. In this work, several classes of problems are considered. For each class, reliable and efficient polytope, n-cube, and n-ball inner approximations are presented. The interval approaches usually proposed are inefficient because they are too computationally heavy for certain applications, such as control. We propose efficient new inner approximation theorems for the considered classes of problems. This allows for usage with real-time applications as well as rapid analysis of potential designs. Several applications are presented for a redundant planar manipulator including locally evaluating the manipulator's velocity, acceleration, and static force capabilities, and evaluating its future acceleration capabilities over a given time horizon

Interval analysis and robotics

International audienceWhen dealing with complex mobile robots, we often have to solve a huge set of nonlinear equations. They may be related to some measurements collected by sensors, to some prior knowledge on the environment or to the differential equations describing the evolution of the robot. For a large class of robots these equations are uncertain, enclose many unknown variables, are strongly nonlinear and should be solved very quickly