POMDP manipulation via trajectory optimization

Efficient object manipulation based only on force feedback typically requires a plan of actively contact-seeking actions to reduce uncertainty over the true environmental model. In principle, that problem could be formulated as a full partially observable Markov decision process (POMDP) whose observations are sensed forces indicating the presence/absence of contacts with objects. Such a naive application leads to a very large POMDP with high-dimensional continuous state, action and observation spaces. Solving such large POMDPs is practically prohibitive. In other words, we are facing three challenging problems: 1) uncertainty over discontinuous contacts with objects; 2) high-dimensional continuous spaces; 3) optimization for not only trajectory cost but also execution time. As trajectory optimization is a powerful model-based method for motion generation, it can handle the last two issues effectively by computing locally optimal trajectories. This paper aims to integrate advantages of trajectory optimization into existing POMDP solvers. The full POMDP formulation is solved using sample-based approaches, where each sampled model is quickly evaluated via trajectory optimization instead of simulating a large number of rollouts. To further accelerate the solver, we propose to integrate temporal abstraction, i. e. macro actions or temporal actions, into the POMDP model. We demonstrate the proposed method on a simulated 7 DoF KUKA arm and a physical Willow Garage PR2 platform. The results show that our proposed method could effectively seek contacts in complex scenarios, and achieve near-optimal performance of path planing.

Authors

• Ngo Anh Vien
• Marc Toussaint

Keywords

• Trajectory optimization
• Robot sensing systems
• Uncertainty
• Computational modeling
• State Space
• Path Planning
• Observation Space
• Advanced Optimization
• Continuous State Space
• High-dimensional State Space
• Executive Function
• Value Function
• Inequality Constraints
• Function Approximation
• Constrained Optimization
• Transition Function
• Size Table
• Bellman Equation
• Time Slice
• Starting State
• Height Information
• Smooth Trajectory
• Linear Quadratic Regulator
• Physical Robot
• Joint Configuration
• Stochastic Optimal Control
• Table Height
• Sampling-based Methods
• Simulated Robot
• Position Table
• External Environment
• Cost Term