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

Lara Brudermüller, Guillaume Berger, Julius Jankowski, Raunak Bhattacharyya, Raphaël Jungers, Nick Hawes

Abstract: Safety in the face of uncertainty is a key challenge in robotics. In this work, we propose a real-time capable framework to generate safe and task-efficient robot trajectories for stochastic control problems. For that, we first formulate the problem as a chance-constrained optimisation problem, in which the probability of the controlled system to violate a safety constraint is constrained to be below a user-defined threshold. To solve the chance-constrained optimisation problem, we propose a Monte-Carlo approximation relying on samples of the uncertainty to estimate the probability of violating a safety constraint given a controller. We use this approximation in the motion planner VP-STO to solve the sampled-based problem. Consequently, we refer to our adapted approach as CC-VPSTO, which stands for Chance-Constrained VP-STO. We address the crucial issue concerning the Monte-Carlo approximation: given a predetermined number of uncertainty samples, we propose several ways to define the sample-based problem such that it is a reliable over-approximation of the original problem, i.e. any solution to the sample-based problem adheres to the original chance-constrained problem with high confidence. The strengths of our approach lie in i) its generality, as it does not require any specific assumptions on the underlying uncertainty distribution, the dynamics of the system, the cost function, and for some of the proposed sample-based approximations, on the form of inequality constraints; and ii) its applicability to MPC-settings. We demonstrate the validity and efficiency of our approach on both simulation and real-world robot experiments.

Paper

This work is making use of our previous work VP-STO, extending it to stochastic control problems:

VP-STO

I. Experiments

Simulation Experiment

Robot task: move from top right to bottom left while the probability of collision with stochastic obstacle(s) in the environment <= eta
Decision variables: via-points of the robot trajectory (cf. VP-STO)
3 different environment configurations with 4-5 obstacles
Range of eta-values: (0.05, 0.2, 0.4, 0.6, 0.8)
1000 experiments for each environment configuration & value of eta
Different environment rollouts in each experiment
Confidence level of 0.95 (beta=0.05) across all experiments
Time-out after 100 MPC steps

Env0

eta=0.05

eta=0.2

eta=0.4

eta=0.6

eta=0.8

Env1

eta=0.05

eta=0.2

eta=0.4

eta=0.6

eta=0.8

Env2

eta=0.05

eta=0.2

eta=0.4

eta=0.6

eta=0.8

Robot Experiment

Box on conveyor belt follows a known stochastic policy from which we can sample
Task: Move ball-shaped EE from one side of conveyor belt to the other side with low probability of collision
We demonstrate CC-VPSTO in an MPC-setting, using 100 particles at
3 Hz
Experiments for various thresholds of eta: 70 runs / threshold

Robot can either pass box behind or in front, not above.

Page updated

Report abuse