Intention-Aware Motion Planning

Intention-aware motion planning

Motivation: Motion planning with uncertainty in human intention.
Assumptions

1. A finite set of unknown intentions.
2. Given intention, the agent’s dynamics is modeled and known to robot.
3. The agent has perfect information on the robot’s and its own state.

Idea:

1. Model intent-aware motion planning as a Partially Observable Markov Decision Process.
2. The agent’s intention is the primary uncertainty state variable in MOMDP.

Preliminaries

1. MDP allows to model action uncertainty only and the state is fully obserable.
2. POMDP specifies p(o|s’,a), which models observation uncertainty.
3. In POMDP, state is not known and is represented as a belief b(s).
4. A POMDP policy induces a value function mapping from b to reward.
5. Each alpha-vector defines a hyperplane over B. The value function V can be represented as a finite set of hyperplanes.

Method

1. In the offline stage, construct a motion model for each agent intention; in the online stage, infer over a finite set of agent intentions and act accordingly.
2. Modelling
   1. Each intention type corresponds to an agent policy $\rou: XxYx\theta$.
   2. $\rou$ can be computed by solving a simplified MDP. Assume the pedestrian follows shortest path and avoids collision.
3. Execution
   1. MOMDP policy, represented as a value function $V(x, y, b_\theta)$.
   2. First selects an action for current belief: $V(x, y, b_\theta) = max_{a} {a * b_\theta}$
   3. Then update the belief: $b’\theta = Z(x’,y’, o) \sum{\theta}{T_x(x, a, x’) * T_y{x, y, \theta, y’} * b(\theta)}$