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This work contributes to a compositional theory of “codesign” that allows to optimally design a robotic platform. In this framework, the user describes each subsystem as a monotone relation between “functionality” provided and “resources” required. These models can be easily composed to express the codesign constraints among different subsystems. The user then queries the model to obtain the design with minimal resources usage, subject to a lower bound on the provided functionality. This letter concerns the introduction of uncertainty in the framework. Uncertainty has two roles: First, it allows to deal with limited knowledge of the models; second, it also can be used to generate consistent relaxations of a problem, as the computation requirements can be lowered, should the user accept some uncertainty in the answer.

Co-design problems in the field of robotics involve the tradeoff of “resources” usage, such as cost, execution time, and energy, with mission performance, under recursive constraints that involve energetics, mechanics, computation, and communication. This letter shows that a large class of codesign problems have a common structure, as they are described by two posets, representing functionality, and resources. The codesign constraints can be expressed as two maps in opposite directions between the two posets. Finding the most resource-economical feasible solution is equivalent to finding the least fixed point of the composition of those two maps. If the two maps are monotone, results from order theory allow concluding uniqueness and systematically deriving an optimal design or a certificate for infeasibility.

Consider a differential-drive mobile robot equipped with an on-board exteroceptive sensor that can estimate its own motion, e.g., a range-finder. Calibration of this robot involves estimating six parameters: three for the odometry (radii and distance between the wheels), and three for the pose of the sensor with respect to the robot. After analyzing the observability of this problem, this paper describes a method for calibrating all parameters at the same time, without the need for external sensors or devices, using only the measurement of the wheels velocities and the data from the exteroceptive sensor. The method does not require the robot to move along particular trajectories. Simultaneous calibration is formulated as a maximum-likelihood problem and the solution is found in a closed form. Experimental results show that the accuracy of the proposed calibration method is very close to the attainable limit given by the Cramér–Rao bound.

This technical note shows that the stationary distribution for the covariance of Kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models (semi-Markov chain). These results are proved using the geometric properties of Riccati recursions with respect to a particular Riemannian distance. Moreover, the Riemannian mean induced by that distance is always bounded, therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist. Other interesting properties of that mean include the symmetry between covariance and information matrices (averaging covariances or their inverse gives the same result), and its interpretation in information geometry as the “natural” mean for the manifold of Gaussian distributions.