Probabilistic Collision Checking with Chance Constraints

Abstract-Obstacle avoidance, and by extension collision checking, is a basic requirement for robot autonomy. Most classical approaches to collision checking ignore the uncertainties associated with the robot and obstacle's geometry and position. It is natural to use a probabilistic description of the uncertainties. However, constraint satisfaction cannot be guaranteed in this case and collision constraints must instead be converted to chance constraints. Standard results for linear probabilistic constraint evaluation have been applied to probabilistic collision evaluation, but this approach ignores the uncertainty associated with the sensed obstacle. An alternative formulation of probabilistic collision checking that accounts for robot and obstacle uncertainty is presented which allows for dependent object distributions (e.g., interactive robotobstacle models). In order to efficiently enforce the resulting collision chance constraints, an approximation is proposed and the validity of this approximation is evaluated. The results presented here have been applied to robot motion planning in dynamic, uncertain environments

CollisionGP: probabilistic collision checking with Gaussian processes

[Resumen] La comprobación de colisiones es la operación primitiva de la planificación de movimientos que más tiempo consume. Se ha demostrado que los algoritmos de aprendizaje automático aceleran la comprobación de colisiones. Presentamos CollisionGP, un algoritmo basado en procesos gaussianos para modelar el espacio de configuraciones de un robot y comprobar colisiones. CollisionGP introduce una variable auxiliar Pòlya-Gamma para cada punto de datos en el conjunto de entrenamiento para permitir que la inferencia de clasificación se realice exactamente con una expresión de forma cerrada. Los procesos gaussianos proporcionan una distribución como salida, obteniendo una media y una varianza para la comprobación de colisión. La varianza obtenida se procesa para reducir los falsos negativos (FN). Demostramos que CollisionGP puede utilizar la aceleración de la GPU para procesar comprobaciones de colisiones para miles de configuraciones mucho más rápido que las librerías tradicionales de detección de colisiones. Además, obtenemos mejores resultados de precisión, ratio de verdaderos positivos (TPR) y verdaderos positivos (TNR) que los algoritmos del estado del arte basados en aprendizaje utilizando menos puntos de soporte, lo que hace que nuestro método sea más ligero.[Abstract] Collision checking is the primitive operation of motion planning that consumes most time. Machine learning algorithms have proven to accelerate collision checking. We propose CollisionGP, a Gaussian process-based algorithm for modeling a robot’s configuration space and query collision checks. CollisionGP introduces a P`olya-Gamma auxiliary variable for each data point in the training set to allow classification inference to be done exactly with a closed-form expression. Gaussian processes provide a distribution as the output, obtaining a mean and variance for the collision check. The obtained variance is processed to reduce false negatives (FN). We demonstrate that CollisionGP can use GPU acceleration to process collision checks for thousands of configurations much faster than traditional collision detection libraries. Furthermore, we obtain better accuracy, true positive rate (TPR) and true negative rate (TNR) results than state-of-the-art learning-based algorithms using less support points, thus making our proposed method more sparse.Comunidad de Madrid; S2018/NMT-433

Fast probabilistic collision checking for sampling-based motion planning using locality-sensitive hashing

We present a novel approach to perform fast probabilistic collision checking in high-dimensional configuration spaces to accelerate the performance of sampling-based motion planning. Our formulation stores the results of prior collision queries, and then uses such information to predict the collision probability for a new configuration sample. In particular, we perform an approximate k-NN ( k-nearest neighbor) search to find prior query samples that are closest to the new query configuration. The new query sample’s collision status is then estimated according to the collision checking results of these prior query samples, based on the fact that nearby configurations are likely to have the same collision status. We use locality-sensitive hashing techniques with sub-linear time complexity for approximate k-NN queries. We evaluate the benefit of our probabilistic collision checking approach by integrating it with a wide variety of sampling-based motion planners, including PRM (Probabilistic roadmaps), lazyPRM, RRT Rapidly exploring random trees, and RRT*. Our method can improve these planners in various manners, such as accelerating the local path validation, or computing an efficient order for the graph search on the roadmap. Experiments on a set of benchmarks demonstrate the performance of our method, and we observe up to 2x speedup in the performance of planners on rigid and articulated robots. </jats:p

Moment-Sum-Of-Squares Approach For Fast Risk Estimation In Uncertain Environments

In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this problem, an unsafe set is described by level sets of polynomials that is, in general, a non-convex set. Uncertainty arises due to the probabilistic parameters of the unsafe set and probabilistic states of the robot. To solve this problem, we use a moment-based representation of probability distributions. We describe upper and lower bounds of the risk in terms of a linear weighted sum of the moments. Weights are coefficients of a univariate Chebyshev polynomial obtained by solving a sum-of-squares optimization problem in the offline step. Hence, given a finite number of moments of probability distributions, risk can be estimated in real-time. We demonstrate the performance of the provided approach by solving probabilistic collision checking problems where we aim to find the probability of collision of a robot with a non-convex obstacle in the presence of probabilistic uncertainties in the location of the robot and size, location, and geometry of the obstacle.Comment: 57th IEEE Conference on Decision and Control 201

Chance-Constrained Multi-Robot Motion Planning under Gaussian Uncertainties

We consider a chance-constrained multi-robot motion planning problem in the presence of Gaussian motion and sensor noise. Our proposed algorithm, CC-K-CBS, leverages the scalability of kinodynamic conflict-based search (K-CBS) in conjunction with the efficiency of the Gaussian belief trees used in the Belief-A framework, and inherits the completeness guarantees of Belief-A's low-level sampling-based planner. We also develop three different methods for robot-robot probabilistic collision checking, which trade off computation with accuracy. Our algorithm generates motion plans driving each robot from its initial state to its goal while accounting for the evolution of its uncertainty with chance-constrained safety guarantees. Benchmarks compare computation time to conservatism of the collision checkers, in addition to characterizing the performance of the planner as a whole. Results show that CC-K-CBS can scale up to 30 robots.Comment: Submitted to 2023 IEEE International Conference on Intelligent Robots and Systems (IROS