Intent-Aware Probabilistic Trajectory Estimation for Collision Prediction with Uncertainty Quantification

Abstract

Collision prediction in a dynamic and unknown environment relies on knowledge of how the environment is changing. Many collision prediction methods rely on deterministic knowledge of how obstacles are moving in the environment. However, complete deterministic knowledge of the obstacles' motion is often unavailable. This work proposes a Gaussian process based prediction method that replaces the assumption of deterministic knowledge of each obstacle's future behavior with probabilistic knowledge, to allow a larger class of obstacles to be considered. The method solely relies on position and velocity measurements to predict collisions with dynamic obstacles. We show that the uncertainty region for obstacle positions can be expressed in terms of a combination of polynomials generated with Gaussian process regression. To control the growth of uncertainty over arbitrary time horizons, a probabilistic obstacle intention is assumed as a distribution over obstacle positions and velocities, which can be naturally included in the Gaussian process framework. Our approach is demonstrated in two case studies in which (i), an obstacle overtakes the agent and (ii), an obstacle crosses the agent's path perpendicularly. In these simulations we show that the collision can be predicted despite having limited knowledge of the obstacle's behavior.

Intent-Aware Optimal Collision Avoidance and Trajectory Planning for a Pursuit Vehicle

“…A real-valued Hamiltonian function H is constructed as in (7). At any t ∈ [0, T int ], if the constraints (2), ( 3) and ( 4) are satisfied, then the Hamiltonian H reaches its maxima and incurs a minimal cost:…”

“…A target is assumed to move linearly along y-axis from (7,6) m with a constant velocity of 0.2 m/s. The pursuer starts tracking the target from (3,3) m and attempts to intercept after 5 s.…”

“…A hybrid model composed of deterministic polynomials and Gaussian distribution of obstacle positions has been proposed in ref. [7].…”

Bernstein Polynomial-Based Method for Solving Optimal Trajectory Generation Problems

“…The predicted trajectory of the opponent is represented as the Bernstein polynomial O n (t) and the minimum safe distance to the opponent is d s . Using a sensor such as a camera or LiDAR, one could measure the state of the opponent and then predict its future position using a method such as the one presented in [49]. At time t = t 0 , when planning occurs, the position of the vehicle is [5,0] m, its speed is 50 m s , and its initial heading angle is π 2 rad.…”

Proximity Queries for Absolutely Continuous Parametric Curves

“…This ability to rapidly compute the feasibility of trajectories allow for a large sample size of trajectories to be validated in a very short amount of time. In addition, these methods prove beneficial for predicting collisions in dynamic environments wherein only probabilistic information of the obstacle behavior is available [27] by computing proximity queries with the boundary of the confidence region of an obstacle's trajectory.…”