Chance-Constrained Via-Point-based Stochastic Trajectory Optimisation for Online Robot Motion Planning under Uncertainty
Lara Brudermüller, Guillaume Berger, Julius Jankowski, Raunak Bhattacharyya, Sylvain Calinon, Raphaël Jungers, Nick Hawes
Abstract: Reliable robot autonomy hinges on decision-making systems that account for uncertainty without imposing overly conservative restrictions on the robot's action space.
We introduce Chance-Constrained Via-Point-Based Stochastic Trajectory Optimisation (CC-VPSTO), a real-time capable framework for generating task-efficient robot trajectories that satisfy constraints with high probability by formulating stochastic control as a chance-constrained optimisation problem. Since such problems are generally intractable, we propose a deterministic surrogate formulation based on Monte Carlo sampling, solved efficiently with gradient-free optimisation. To address bias in naïve sampling approaches, we quantify approximation error and introduce padding strategies to improve reliability. We focus on three challenges: (i) sample-efficient constraint approximation, (ii) conditions for surrogate solution validity, and (iii) online optimisation. Integrated into a receding-horizon MPC framework, CC-VPSTO enables reactive and task-efficient control under uncertainty. The strengths of our approach lie in its generality, i.e. no assumptions on the underlying uncertainty distribution, system dynamics, cost function, or the form of inequality constraints; and its applicability to online robot motion planning. We demonstrate the validity and efficiency of our approach in both simulation and on a Franka Emika robot.
This work is making use of our previous work VP-STO, extending it to stochastic control problems:
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
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.
