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.

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.

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.

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.

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.

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 prob-lem 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.

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.

When predicting trajectories of road agents, motion predictors often 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 during training. The task utility function is commonly used to evaluate task performance. It does not require the full task information, but rather a specification of the utility of the task, resulting in predictors that are tailored to different 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.

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.

Real-world environments are inherently uncertain, and to operate safely in these environments robots must be able to plan around this uncertainty. In the context of motion planning, we desire systems that can maintain an acceptable level of safety as the robot moves, even when the exact locations of nearby obstacles are not known. In this paper, we solve this chance-constrained motion planning problem using a sequential convex optimization framework. To constrain the risk of collision incurred by planned movements, we employ geometric objects called ε-shadows to compute upper bounds on the risk of collision between the robot and uncertain obstacles. We use these ε-shadow-based estimates as constraints in a nonlinear trajectory optimization problem, which we then solve by iteratively linearizing the non-convex risk constraints. This sequential optimization approach quickly finds trajectories that accomplish the desired motion while maintaining a user-specified limit on collision risk. Our method can be applied to robots and environments with arbitrary convex geometry; even in complex environments, it runs in less than a second and provides provable guarantees on the safety of planned trajectories, enabling fast, reactive, and safe robot motion in realistic environments.

This paper introduces Probabilistic Chekov (p-Chekov), a chance-constrained motion planning system that can be applied to high degree-of-freedom (DOF) robots under motion uncertainty and imperfect state information. Given process and observation noise models, it can find feasible trajectories which satisfy a user-specified bound over the probability of collision. Leveraging our previous work in deterministic motion planning which integrated trajectory optimization into a sparse roadmap framework, p-Chekov shows superiority in its planning speed for high-dimensional tasks. P-Chekov incorporates a linear-quadratic Gaussian motion planning approach into the estimation of the robot state probability distribution, applies quadrature theories to waypoint collision risk estimation, and adapts risk allocation approaches to assign allowable probabilities of failure among waypoints. Unlike other existing risk-aware planners, p-Chekov can be applied to high-DOF robotic planning tasks without the convexification of the environment. The experiment results in this paper show that this p-Chekov system can effectively reduce collision risk and satisfy user-specified chance constraints in typical real-world planning scenarios for high-DOF robots.

Partially Observable Markov Decision Process (POMDP) is a fundamental framework for planning and decision making under uncertainty. POMDP is known to be intractable to solve or even approximate when the planning horizon is long (i.e., within a polynomial number of time steps). Constrained POMDP (C-POMDP) allows constraints to be specified on some aspects of the policy in addition to the objective function. When the constraints involve bounding the probability of failure, the problem is called Chance-Constrained POMDP (CC-POMDP). Our first contribution is a reduction from CC-POMDP to C-POMDP and a novel Integer Linear Programming (ILP) formulation. Thus, any algorithm for the later problem can be utilized to solve any instance of the former. Second, we show that unlike POMDP, when the length of the planning horizon is constant, (C)C-POMDP is NP-Hard. Third, we present the first Fully Polynomial Time Approximation Scheme (FPTAS) that computes (near) optimal deterministic policies for constant-horizon (C)C-POMDP in polynomial time.