Chance-Constrained Via-Point-based Stochastic Trajectory Optimisation for Safe and Efficient Online Robot Motion Planning

Core Concepts

A real-time capable framework to generate safe and task-efficient robot trajectories for stochastic control problems by formulating the problem as a chance-constrained optimisation and solving it using a Monte-Carlo approximation.

Abstract

The paper introduces a chance-constrained optimisation framework called CC-VPSTO for generating safe and efficient robot trajectories in the presence of uncertainty. The key contributions are:

A Monte-Carlo approach to approximate the chance constraint, which allows handling arbitrary uncertainty models. This is integrated into the VP-STO motion planner.

Theoretical and empirical guarantees on the correctness of the approach, providing confidence bounds on the satisfaction of the true chance constraint.

A formulation suitable for Model Predictive Control (MPC), enabling safe real-time robot control.

Evaluations in simulation and real-world experiments on a Franka Emika robot arm, demonstrating the validity and efficiency of the approach.

The core advantages are the flexibility to handle various uncertainty models, the real-time applicability, and the ability to handle any type of inequality constraint within the chance constraint.
The offline planning experiments show that the proposed heuristic ηbinom provides a good approximation of the true chance constraint, with the empirical probability of constraint violation ˆβ matching the user-defined confidence level. The online MPC experiments demonstrate the real-time capability of the approach, with the robot successfully navigating a dynamic environment with stochastic obstacles.

Stats

The robot has to move its ball-shaped end effector from a start point to a goal point on a conveyor belt, while avoiding a box obstacle on the moving conveyor belt.
The box obstacle's motion is controlled according to a stochastic policy.

Quotes

"Safety in the face of uncertainty is a key challenge in robotics."
"Chance-constrained optimisation generalises the above by allowing constraints that depend on a random variable."
"A core advantage of chance-constrained formulations is their flexibility, making them suitable for a wide range of uncertainty models."

Key Insights Distilled From

CC-VPSTO

by Lara... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2402.01370.pdf

Deeper Inquiries

How could the proposed framework be extended to handle multiple chance constraints, e.g., collision avoidance and task completion

To extend the proposed framework to handle multiple chance constraints, such as collision avoidance and task completion, we can modify the chance-constrained optimisation problem formulation. We can introduce additional inequality constraints that represent each chance constraint, ensuring that the probability of violating each constraint is below the specified threshold. For example, if we have a collision avoidance constraint and a task completion constraint, we can include both constraints in the optimisation problem:
minimize J(x)
subject to:

P(G_collision = 1) <= η_collision
P(G_task_completion = 1) <= η_task_completion
Here, G_collision and G_task_completion are binary random variables representing the violation of the collision avoidance and task completion constraints, respectively. By solving this modified optimisation problem, we can generate trajectories that not only avoid collisions with high probability but also achieve the task with a specified likelihood.

What are the limitations of the independence assumption in the Bernoulli process approximation, and how could it be relaxed further

The independence assumption in the Bernoulli process approximation can be relaxed further by considering the correlation between the samples. One way to address this limitation is to incorporate a dependency structure among the samples, especially when evaluating the constraint violation probability for a candidate solution. This can be achieved by using techniques from probabilistic graphical models or sequential Monte Carlo methods, which capture the temporal or spatial dependencies in the uncertainty samples. By modeling the dependencies between samples, we can improve the accuracy of the chance constraint approximation and provide more reliable estimates of the constraint violation probability.

Could the chance-constrained optimisation be combined with learning-based techniques to improve the modelling of the stochastic environment dynamics

Combining chance-constrained optimisation with learning-based techniques can enhance the modelling of stochastic environment dynamics and improve the performance of the system. One approach is to use reinforcement learning to adapt the chance constraint thresholds based on the system's performance and feedback from the environment. By learning the optimal thresholds for the chance constraints, the system can dynamically adjust its risk tolerance and decision-making process in uncertain environments. Additionally, machine learning algorithms can be used to model the uncertainty distribution more accurately, allowing for better estimation of the probability of constraint violation and improving the overall robustness of the system. By integrating learning-based techniques with chance-constrained optimisation, the system can adapt and optimize its behavior in complex and changing environments.