arXiv subjects

Ashkan Jasour

Publications and source records attributed to Ashkan Jasour.

At least 19 recordsLinked to original sources

arXiv2025

Max Entropy Moment Kalman Filter for Polynomial Systems with Arbitrary Noise

Designing optimal Bayes filters for nonlinear non-Gaussian systems is a challenging task. The main difficulties are: 1) representing complex beliefs, 2) handling non-Gaussian noise, and 3) marginalizing past states. To address these challenges, we focus on polynomial systems and propose the Max Entropy Moment Kalman Filter (MEM-KF). To address 1), we represent arbitrary beliefs by a Moment-Constrained Max-Entropy Distribution (MED). The MED can asymptotically approximate almost any distribution given an increasing number of moment constraints. To address 2), we model the noise in the process and observation model as MED. To address 3), we propagate the moments through the process model and recover the distribution as MED, thus avoiding symbolic integration, which is generally intractable. All the steps in MEM-KF, including the extraction of a point estimate, can be solved via convex optimization. We showcase the MEM-KF in challenging robotics tasks, such as localization with unknown data association.

cs.RO↗

arXiv2025

Risk-aware Integrated Task and Motion Planning for Versatile Snake Robots under Localization Failures

Snake robots enable mobility through extreme terrains and confined environments in terrestrial and space applications. However, robust perception and localization for snake robots remain an open challenge due to the proximity of the sensor payload to the ground coupled with a limited field of view. To address this issue, we propose Blind-motion with Intermittently Scheduled Scans (BLISS) which combines proprioception-only mobility with intermittent scans to be resilient against both localization failures and collision risks. BLISS is formulated as an integrated Task and Motion Planning (TAMP) problem that leads to a Chance-Constrained Hybrid Partially Observable Markov Decision Process (CC-HPOMDP), known to be computationally intractable due to the curse of history. Our novelty lies in reformulating CC-HPOMDP as a tractable, convex Mixed Integer Linear Program. This allows us to solve BLISS-TAMP significantly faster and jointly derive optimal task-motion plans. Simulations and hardware experiments on the EELS snake robot show our method achieves over an order of magnitude computational improvement compared to state-of-the-art POMDP planners and $>$ 50\% better navigation time optimality versus classical two-stage planners.

cs.RO↗

arXiv2024

GMKF: Generalized Moment Kalman Filter for Polynomial Systems with Arbitrary Noise

This paper develops a new filtering approach for state estimation in polynomial systems corrupted by arbitrary noise, which commonly arise in robotics. We first consider a batch setup where we perform state estimation using all data collected from the initial to the current time. We formulate the batch state estimation problem as a Polynomial Optimization Problem (POP) and relax the assumption of Gaussian noise by specifying a finite number of moments of the noise. We solve the resulting POP using a moment relaxation and prove that under suitable conditions on the rank of the relaxation, (i) we can extract a provably optimal estimate from the moment relaxation, and (ii) we can obtain a belief representation from the dual (sum-of-squares) relaxation. We then turn our attention to the filtering setup and apply similar insights to develop a GMKF for recursive state estimation in polynomial systems with arbitrary noise. The GMKF formulates the prediction and update steps as POPs and solves them using moment relaxations, carrying over a possibly non-Gaussian belief. In the linear-Gaussian case, GMKF reduces to the standard Kalman Filter. We demonstrate that GMKF performs well under highly non-Gaussian noise and outperforms common alternatives, including the Extended and Unscented Kalman Filter, and their variants on matrix Lie group.

cs.RO↗

arXiv2024

Peak Value-at-Risk Estimation of Stochastic Processes using Occupation Measures

This paper formulates algorithms to upper-bound the maximum Value-at-Risk (VaR) of a state function along trajectories of stochastic processes. The VaR is upper bounded by two methods: minimax tail-bounds (Cantelli/Vysochanskij-Petunin) and Expected Shortfall/Conditional Value-at-Risk (ES). Tail-bounds lead to a infinite-dimensional Second Order Cone Program (SOCP) in occupation measures, while the ES approach creates a Linear Program (LP) in occupation measures. Under compactness and regularity conditions, there is no relaxation gap between the infinite-dimensional convex programs and their nonconvex optimal-stopping stochastic problems. Upper-bounds on the SOCP and LP are obtained by a sequence of semidefinite programs through the moment-Sum-of-Squares hierarchy. The VaR-upper-bounds are demonstrated on example continuous-time and discrete-time polynomial stochastic processes.

math.OC↗

arXiv2023

Non-Gaussian Uncertainty Minimization Based Control of Stochastic Nonlinear Robotic Systems

In this paper, we consider the closed-loop control problem of nonlinear robotic systems in the presence of probabilistic uncertainties and disturbances. More precisely, we design a state feedback controller that minimizes deviations of the states of the system from the nominal state trajectories due to uncertainties and disturbances. Existing approaches to address the control problem of probabilistic systems are limited to particular classes of uncertainties and systems such as Gaussian uncertainties and processes and linearized systems. We present an approach that deals with nonlinear dynamics models and arbitrary known probabilistic uncertainties. We formulate the controller design problem as an optimization problem in terms of statistics of the probability distributions including moments and characteristic functions. In particular, in the provided optimization problem, we use moments and characteristic functions to propagate uncertainties throughout the nonlinear motion model of robotic systems. In order to reduce the tracking deviations, we minimize the uncertainty of the probabilistic states around the nominal trajectory by minimizing the trace and the determinant of the covariance matrix of the probabilistic states. To obtain the state feedback gains, we solve deterministic optimization problems in terms of moments, characteristic functions, and state feedback gains using off-the-shelf interior-point optimization solvers. To illustrate the performance of the proposed method, we compare our method with existing probabilistic control methods.

cs.RO↗

arXiv2023

Real-Time Tube-Based Non-Gaussian Risk Bounded Motion Planning for Stochastic Nonlinear Systems in Uncertain Environments via Motion Primitives

We consider the motion planning problem for stochastic nonlinear systems in uncertain environments. More precisely, in this problem the robot has stochastic nonlinear dynamics and uncertain initial locations, and the environment contains multiple dynamic uncertain obstacles. Obstacles can be of arbitrary shape, can deform, and can move. All uncertainties do not necessarily have Gaussian distribution. This general setting has been considered and solved in [1]. In addition to the assumptions above, in this paper, we consider long-term tasks, where the planning method in [1] would fail, as the uncertainty of the system states grows too large over a long time horizon. Unlike [1], we present a real-time online motion planning algorithm. We build discrete-time motion primitives and their corresponding continuous-time tubes offline, so that almost all system states of each motion primitive are guaranteed to stay inside the corresponding tube. We convert probabilistic safety constraints into a set of deterministic constraints called risk contours. During online execution, we verify the safety of the tubes against deterministic risk contours using sum-of-squares (SOS) programming. The provided SOS-based method verifies the safety of the tube in the presence of uncertain obstacles without the need for uncertainty samples and time discretization in real-time. By bounding the probability the system states staying inside the tube and bounding the probability of the tube colliding with obstacles, our approach guarantees bounded probability of system states colliding with obstacles. We demonstrate our approach on several long-term robotics tasks.

cs.RO↗

arXiv2023

Convex Risk Bounded Continuous-Time Trajectory Planning and Tube Design in Uncertain Nonconvex Environments

In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded trajectory planning method that looks for continuous-time trajectories with guaranteed bounded risk over the planning time horizon. Risk is defined as the probability of collision with uncertain obstacles. Existing approaches to address risk bounded trajectory planning problems either are limited to Gaussian uncertainties and convex obstacles or rely on sampling-based methods that need uncertainty samples and time discretization. To address the risk bounded trajectory planning problem, we leverage the notion of risk contours to transform the risk bounded planning problem into a deterministic optimization problem. Risk contours are the set of all points in the uncertain environment with guaranteed bounded risk. The obtained deterministic optimization is, in general, nonlinear and nonconvex time-varying optimization. We provide convex methods based on sum-of-squares optimization to efficiently solve the obtained nonconvex time-varying optimization problem and obtain the continuous-time risk bounded trajectories without time discretization. The provided approach deals with arbitrary (and known) probabilistic uncertainties, nonconvex and nonlinear, static and dynamic obstacles, and is suitable for online trajectory planning problems. In addition, we provide convex methods based on sum-of-squares optimization to build the max-sized tube with respect to its parameterization along the trajectory so that any state inside the tube is guaranteed to have bounded risk.

cs.AI↗

arXiv2023

Convex Geometric Motion Planning on Lie Groups via Moment Relaxation

This paper reports a novel result: with proper robot models on matrix Lie groups, one can formulate the kinodynamic motion planning problem for rigid body systems as \emph{exact} polynomial optimization problems that can be relaxed as semidefinite programming (SDP). Due to the nonlinear rigid body dynamics, the motion planning problem for rigid body systems is nonconvex. Existing global optimization-based methods do not properly deal with the configuration space of the 3D rigid body; thus, they do not scale well to long-horizon planning problems. We use Lie groups as the configuration space in our formulation and apply the variational integrator to formulate the forced rigid body systems as quadratic polynomials. Then we leverage Lasserre's hierarchy to obtain the globally optimal solution via SDP. By constructing the motion planning problem in a sparse manner, the results show that the proposed algorithm has \emph{linear} complexity with respect to the planning horizon. This paper demonstrates the proposed method can provide rank-one optimal solutions at relaxation order two for most of the testing cases of 1) 3D drone landing using the full dynamics model and 2) inverse kinematics for serial manipulators.

cs.RO↗

arXiv2023

Chance-Constrained Trajectory Optimization for High-DOF Robots in Uncertain Environments

Many practical applications of robotics require systems that can operate safely despite uncertainty. In the context of motion planning, two types of uncertainty are particularly important when planning safe robot trajectories. The first is environmental uncertainty -- uncertainty in the locations of nearby obstacles, stemming from sensor noise or (in the case of obstacles' future locations) prediction error. The second class of uncertainty is uncertainty in the robots own state, typically caused by tracking or estimation error. To achieve high levels of safety, it is necessary for robots to consider both of these sources of uncertainty. In this paper, we propose a risk-bounded trajectory optimization algorithm, known as Sequential Convex Optimization with Risk Optimization (SCORA), to solve chance-constrained motion planning problems despite both environmental uncertainty and tracking error. Through experiments in simulation, we demonstrate that SCORA significantly outperforms state-of-the-art risk-aware motion planners both in planning time and in the safety of the resulting trajectories.

cs.RO↗

arXiv2023

Moment-based Kalman Filter: Nonlinear Kalman Filtering with Exact Moment Propagation

This paper develops a new nonlinear filter, called Moment-based Kalman Filter (MKF), using the exact moment propagation method. Existing state estimation methods use linearization techniques or sampling points to compute approximate values of moments. However, moment propagation of probability distributions of random variables through nonlinear process and measurement models play a key role in the development of state estimation and directly affects their performance. The proposed moment propagation procedure can compute exact moments for non-Gaussian as well as non-independent Gaussian random variables. Thus, MKF can propagate exact moments of uncertain state variables up to any desired order. MKF is derivative-free and does not require tuning parameters. Moreover, MKF has the same computation time complexity as the extended or unscented Kalman filters, i.e., EKF and UKF. The experimental evaluations show that MKF is the preferred filter in comparison to EKF and UKF and outperforms both filters in non-Gaussian noise regimes.

cs.RO↗

arXiv2022

A Closed-Form Uncertainty Propagation in Non-Rigid Structure from Motion

Semi-Definite Programming (SDP) with low-rank prior has been widely applied in Non-Rigid Structure from Motion (NRSfM). Based on a low-rank constraint, it avoids the inherent ambiguity of basis number selection in conventional base-shape or base-trajectory methods. Despite the efficiency in deformable shape reconstruction, it remains unclear how to assess the uncertainty of the recovered shape from the SDP process. In this paper, we present a statistical inference on the element-wise uncertainty quantification of the estimated deforming 3D shape points in the case of the exact low-rank SDP problem. A closed-form uncertainty quantification method is proposed and tested. Moreover, we extend the exact low-rank uncertainty quantification to the approximate low-rank scenario with a numerical optimal rank selection method, which enables solving practical application in SDP based NRSfM scenario. The proposed method provides an independent module to the SDP method and only requires the statistic information of the input 2D tracked points. Extensive experiments prove that the output 3D points have identical normal distribution to the 2D trackings, the proposed method and quantify the uncertainty accurately, and supports that it has desirable effects on routinely SDP low-rank based NRSfM solver.

cs.CV↗

arXiv2022

TIP: Task-Informed Motion Prediction for Intelligent Vehicles

When predicting trajectories of road agents, motion predictors usually approximate the future distribution by a limited number of samples. This constraint requires the predictors to generate samples that best support the task given task specifications. However, existing predictors are often optimized and evaluated via task-agnostic measures without accounting for the use of predictions in downstream tasks, and thus could result in sub-optimal task performance. In this paper, we propose a task-informed motion prediction model that better supports the tasks through its predictions, by jointly reasoning about prediction accuracy and the utility of the downstream tasks, which is commonly used to evaluate the task performance. The task utility function does not require the full task information, but rather a specification of the utility of the task, resulting in predictors that serve a wide range of downstream tasks. We demonstrate our approach on two use cases of common decision making tasks and their utility functions, in the context of autonomous driving and parallel autonomy. Experiment results show that our predictor produces accurate predictions that improve the task performance by a large margin in both tasks when compared to task-agnostic baselines on the Waymo Open Motion dataset.

cs.RO↗

arXiv2022

Non-Gaussian Risk Bounded Trajectory Optimization for Stochastic Nonlinear Systems in Uncertain Environments

We address the risk bounded trajectory optimization problem of stochastic nonlinear robotic systems. More precisely, we consider the motion planning problem in which the robot has stochastic nonlinear dynamics and uncertain initial locations, and the environment contains multiple dynamic uncertain obstacles with arbitrary probabilistic distributions. The goal is to plan a sequence of control inputs for the robot to navigate to the target while bounding the probability of colliding with obstacles. Existing approaches to address risk bounded trajectory optimization problems are limited to particular classes of models and uncertainties such as Gaussian linear problems. In this paper, we deal with stochastic nonlinear models, nonlinear safety constraints, and arbitrary probabilistic uncertainties, the most general setting ever considered. To address the risk bounded trajectory optimization problem, we first formulate the problem as an optimization problem with stochastic dynamics equations and chance constraints. We then convert probabilistic constraints and stochastic dynamics constraints on random variables into a set of deterministic constraints on the moments of state probability distributions. Finally, we solve the resulting deterministic optimization problem using nonlinear optimization solvers and get a sequence of control inputs. To our best knowledge, it is the first time that the motion planning problem to such a general extent is considered and solved. To illustrate the performance of the proposed method, we provide several robotics examples.

cs.RO↗

arXiv2021

HYPER: Learned Hybrid Trajectory Prediction via Factored Inference and Adaptive Sampling

Modeling multi-modal high-level intent is important for ensuring diversity in trajectory prediction. Existing approaches explore the discrete nature of human intent before predicting continuous trajectories, to improve accuracy and support explainability. However, these approaches often assume the intent to remain fixed over the prediction horizon, which is problematic in practice, especially over longer horizons. To overcome this limitation, we introduce HYPER, a general and expressive hybrid prediction framework that models evolving human intent. By modeling traffic agents as a hybrid discrete-continuous system, our approach is capable of predicting discrete intent changes over time. We learn the probabilistic hybrid model via a maximum likelihood estimation problem and leverage neural proposal distributions to sample adaptively from the exponentially growing discrete space. The overall approach affords a better trade-off between accuracy and coverage. We train and validate our model on the Argoverse dataset, and demonstrate its effectiveness through comprehensive ablation studies and comparisons with state-of-the-art models.

cs.RO↗

arXiv2021

Real-Time Risk-Bounded Tube-Based Trajectory Safety Verification

In this paper, we address the real-time risk-bounded safety verification problem of continuous-time state trajectories of autonomous systems in the presence of uncertain time-varying nonlinear safety constraints. Risk is defined as the probability of not satisfying the uncertain safety constraints. Existing approaches to address the safety verification problems under uncertainties either are limited to particular classes of uncertainties and safety constraints, e.g., Gaussian uncertainties and linear constraints, or rely on sampling based methods. In this paper, we provide a fast convex algorithm to efficiently evaluate the probabilistic nonlinear safety constraints in the presence of arbitrary probability distributions and long planning horizons in real-time, without the need for uncertainty samples and time discretization. The provided approach verifies the safety of the given state trajectory and its neighborhood (tube) to account for the execution uncertainties and risk. In the provided approach, we first use the moments of the probability distributions of the uncertainties to transform the probabilistic safety constraints into a set of deterministic safety constraints. We then use convex methods based on sum-of-squares polynomials to verify the obtained deterministic safety constraints over the entire planning time horizon without time discretization. To illustrate the performance of the proposed method, we apply the provided method to the safety verification problem of self-driving vehicles and autonomous aerial vehicles.

cs.RO↗

arXiv2021

Fast nonlinear risk assessment for autonomous vehicles using learned conditional probabilistic models of agent futures

This paper presents fast non-sampling based methods to assess the risk for trajectories of autonomous vehicles when probabilistic predictions of other agents' futures are generated by deep neural networks (DNNs). The presented methods address a wide range of representations for uncertain predictions including both Gaussian and non-Gaussian mixture models to predict both agent positions and control inputs conditioned on the scene contexts. We show that the problem of risk assessment when Gaussian mixture models (GMMs) of agent positions are learned can be solved rapidly to arbitrary levels of accuracy with existing numerical methods. To address the problem of risk assessment for non-Gaussian mixture models of agent position, we propose finding upper bounds on risk using nonlinear Chebyshev's Inequality and sums-of-squares (SOS) programming; they are both of interest as the former is much faster while the latter can be arbitrarily tight. These approaches only require higher order statistical moments of agent positions to determine upper bounds on risk. To perform risk assessment when models are learned for agent control inputs as opposed to positions, we propagate the moments of uncertain control inputs through the nonlinear motion dynamics to obtain the exact moments of uncertain position over the planning horizon. To this end, we construct deterministic linear dynamical systems that govern the exact time evolution of the moments of uncertain position in the presence of uncertain control inputs. The presented methods are demonstrated on realistic predictions from DNNs trained on the Argoverse and CARLA datasets and are shown to be effective for rapidly assessing the probability of low probability events.

cs.LG↗

arXiv2021

Risk Conditioned Neural Motion Planning

Risk-bounded motion planning is an important yet difficult problem for safety-critical tasks. While existing mathematical programming methods offer theoretical guarantees in the context of constrained Markov decision processes, they either lack scalability in solving larger problems or produce conservative plans. Recent advances in deep reinforcement learning improve scalability by learning policy networks as function approximators. In this paper, we propose an extension of soft actor critic model to estimate the execution risk of a plan through a risk critic and produce risk-bounded policies efficiently by adding an extra risk term in the loss function of the policy network. We define the execution risk in an accurate form, as opposed to approximating it through a summation of immediate risks at each time step that leads to conservative plans. Our proposed model is conditioned on a continuous spectrum of risk bounds, allowing the user to adjust the risk-averse level of the agent on the fly. Through a set of experiments, we show the advantage of our model in terms of both computational time and plan quality, compared to a state-of-the-art mathematical programming baseline, and validate its performance in more complicated scenarios, including nonlinear dynamics and larger state space.

cs.LG↗

arXiv2021

Convex Risk Bounded Continuous-Time Trajectory Planning in Uncertain Nonconvex Environments

In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded trajectory planning method that looks for continuous-time trajectories with guaranteed bounded risk over the planning time horizon. Risk is defined as the probability of collision with uncertain obstacles. Existing approaches to address risk bounded trajectory planning problems either are limited to Gaussian uncertainties and convex obstacles or rely on sampling-based methods that need uncertainty samples and time discretization. To address the risk bounded trajectory planning problem, we leverage the notion of risk contours to transform the risk bounded planning problem into a deterministic optimization problem. Risk contours are the set of all points in the uncertain environment with guaranteed bounded risk. The obtained deterministic optimization is, in general, nonlinear and nonconvex time-varying optimization. We provide convex methods based on sum-of-squares optimization to efficiently solve the obtained nonconvex time-varying optimization problem and obtain the continuous-time risk bounded trajectories without time discretization. The provided approach deals with arbitrary probabilistic uncertainties, nonconvex and nonlinear, static and dynamic obstacles, and is suitable for online trajectory planning problems.

cs.RO↗