Optimal control based trajectory generation offers the ability to formulate complex problems while optimizing the performance of the system control inputs. Nevertheless, adding acoustic constraints to the optimal control problem (OCP) can be highly challenging. The classical resolution approach employs a “first-discretize-then-optimize” strategy using direct methods. However, this approach leads to significant computational costs, which in turn limits its applicability. Recent studies suggest using the acoustic reciprocity theorem (ART) to formulate the problem as one of obstacles collision avoidance. Hence, this study proposes investigating the formulation and solution of an OCP based on this theorem. The ART is combined with the Boundary Element Method (BEM) for the acoustic part of the problem. The OCP is implemented using successive convexification (SCvx) approach which offers a convenient framework to take into account acoustic constraint in trajectory planning generation. Promising experimental results highlight the applicability of our formulation based on the ART and guidelines for further development are provided.

The recent development of foundation models for monocular depth estimation such as Depth Anything paved the way to zero-shot monocular depth estimation. Since it returns an affine-invariant disparity map, the favored technique to recover the metric depth consists in fine-tuning the model. However, this stage is not straightforward, it can be costly and time-consuming because of the training and the creation of the dataset. The latter must contain images captured by the camera that will be used at test time and the corresponding ground truth. Moreover, the fine-tuning may also degrade the generalizing capacity of the original model. Instead, we propose in this paper a new method to rescale Depth Anything predictions using 3D points provided by sensors or techniques such as low-resolution LiDAR or structure-from-motion with poses given by an IMU. This approach avoids fine-tuning and preserves the generalizing power of the original depth estimation model while being robust to the noise of the sparse depth, of the camera-LiDAR calibration or of the depth model. Our experiments highlight enhancements relative to zero-shot monocular metric depth estimation methods, competitive results compared to fine-tuned approaches and a better robustness than depth completion approaches. Code available at github.com/ENSTA-U2IS-AI/depth-rescaling.

The use of serial robots for industrial and research purposes is often limited by a flawed positioning accuracy, caused by the differences between the robot nominal model, and the real one. Such an issue can be solved by means of kinematic calibration, which is usually a tedious and intricate task. In this paper, we propose a complete kinematic calibration procedure relying on established geometric modeling, measurements design and parameters identification methods, as well as multiple integration tools, to provide a high adaptability and a simplified handling. The overall process was bundled up in a ROS-based modular and user-friendly package, whose main objective is to offer a smooth and fully integrated framework for the kinematic calibration of serial robots. Our solution was successfully tested using a motion tracking device, and allowed to increase the overall positioning accuracy of two different serial robots by 75% in a matter of hours.

As the scope and complexity of modern cyber-physical systems increase, newer and more challenging mission requirements will be imposed on the optimal control of the underlying unmanned systems. This paper proposes a solution to handle complex temporal requirements formalized in Signal Temporal Logic (STL) specifications within the Successive Convexification (SCvx) algorithmic framework. This SCvx-STL solution method consists of four steps: 1) Express the STL specifications using their robust semantics as state constraints. 2) Introduce new auxiliary state variables to transform these state constraints as system dynamics, by exploiting the recursively defined structure of robust STL semantics. 3) Smooth the resulting system dynamics with polynomial smooth min- and max- functions. 4) Convexify and solve the resulting optimal control problem with the SCvx algorithm, which enjoys guaranteed convergence and polynomial time subproblem solving capability. Our approach retains the expressiveness of encoding mission requirements with STL semantics, while avoiding the usage of combinatorial optimization techniques such as Mixed-integer programming. Numerical results are shown to demonstrate its effectiveness.

Numerical integration schemes are mandatory to understand complex behaviors of dynamical systems described by ordinary differential equations. Implementation of these numerical methods involve floating-point computations and propagation of round-off errors. This paper presents a new fine-grained analysis of round-off errors in explicit Runge-Kutta integration methods, taking into account exceptional behaviors, such as underflow and overflow. Linear stability properties play a central role in the proposed approach. For a large class of Runge-Kutta methods applied on linear problems, a tight bound of the round-off errors is provided. A simple test is defined and ensures the absence of underflow and a tighter round-off error bound. The absence of overflow is guaranteed as linear stability properties imply that (computed) solutions are non-increasing.

Ordinary differential equations are ubiquitous in scientific computing. Solving exactly these equations is usually not possible, except for special cases, hence the use of numerical schemes to get a discretized solution. We are interested in such numerical integration methods, for instance Euler's method or the Runge-Kutta methods. As they are implemented using floating-point arithmetic, round-off errors occur. In order to guarantee their accuracy, we aim at providing bounds on the round-off errors of explicit one-step numerical integration methods. Our methodology is to apply a fine-grained analysis to these numerical algorithms. Our originality is that our floating-point analysis takes advantage of the linear stability of the scheme, a mathematical property that vouches the scheme is well-behaved.

Floating-point numbers are used to approximate the exact real numbers in a wide range of domains like numerical simulations, embedded software, etc. However, floating-point numbers are a finite approximation of real numbers. In practice, this approximation may introduce round-off errors and this can lead to catastrophic results. To cope with this issue, we have developed a tool which corrects partly these round-off errors and which consequently improves the numerical accuracy of computations by automatically transforming programs in a source to source manner. Our transformation, relies on static analysis by abstract interpretation and operates on pieces of code with assignments, conditionals and loops. In former work, we have focused on the intraprocedural transformation of programs and, in this article, we introduce the interprocedural transformation to improve accuracy.

In floating-point arithmetic, a desirable property of computations is to be accurate, since in many industrial context small or large perturbations due to round-off errors may cause considerable damages. To cope with this matter of fact, we have developed a tool which corrects these errors by automatically transforming programs in a source to source manner. Our transformation, relying on static analysis by abstract abstraction, concerns pieces of code with assignments, conditionals and loops. By transforming programs, we can significantly optimize the numerical accuracy of computations by minimizing the error relatively to the exact result. An interesting side-effect of our technique is that more accurate computations may make it possible to use smaller data-types. In this article, we show that our transformed programs, executed in single precision, may compete with not transformed codes executed in double precision.

The industrial tool Matlab/Simulink is widely used in the design of embedded systems. The main feature of this tool is its ability to model in a common formalism the software and its physical environment. This makes it very useful for validating the design of embedded software using numerical simulation. However, the formal verification of such models is still problematic as Simulink is a programming language for which no formal semantics exists. In this article, we present an operational semantics of a representative subset of Simulink which includes both continuous-time and discrete-time blocks. We believe that this work gives a better understanding of Simulink and it defines the foundations of a general framework to apply formal methods on Simulink's high level descriptions of embedded systems.

Hybrid systems are a widely used model to represent and reason about control-command systems. In an industrial context, these are often implemented in Simulink and their validity is checked by performing many numerical simulations in order to test their behavior with various possible inputs. In this article, we present a tool named HySon which performs set-based simulation of hybrid systems with uncertain parameters, expressed in Simulink. Our tool handles advanced features such as non-linear operations, zero-crossing events or discrete sampling. It is based on well-known efficient numerical algorithms that were adapted to handle set-based domains. We demonstrate the performance of our method on various examples.