Safe Motion Planning in Belief Space for Self-Driving Cars

Making safe vehicle decisions and planning of collision-free trajectories play a critical role on the widespread of autonomous vehicles. Decision making and trajectory planning layers constitute the uppermost layer of a typical autonomous vehicle system architecture and therefore, their input comprises a considerable amount of uncertainties that accumulate during perception and situation understanding computations. In order to perform holistic probabilistic processing and thereby to ensure safety, these uncertainties must be processed in belief-space rather than space-state.

Optimization-based Approach

The sources of the uncertainties are diverse. Limited sensor range, harsh weather conditions diminishing the quality of the perception, and occluded objects in the environment are among the most ordinary problems. But furthermore, an autonomous vehicle must also be able to deal with the unexpected behaviour of other traffic participants, which sometimes even unobserve the traffic regulations.



Safe motion in path–time–speed x × t × v space for the intersection scenario. Any motion that is below the blue surface can come to full stop before the intersection. We call the surface of this volume as surface-of-no-return. Any point on this surface, such as the orange point, is the point- of-no-return.

Safe stops

Path-time diagram

Safety analysis on path-time diagram. The blue regions represent the states that are not reachable by the vehicle. The gray region represent the states that are occupied by an obstacle. The thick blue line corresponds to the optimized motion, whereas with "+" denoted points are the full braking stop points of the trajectory support points of the same time-index.

Rule uncompliant traffic participants

An automated vehicle should be able to compensate uncompliant behavior of other traffic participants when approaching to an intersection where it has the right-of-way. While being proactive, it should not move too defensive: its motion must be transparent enough to reflect that it intends to preserve its right-of-way.

Uncertain localization

Uncertain localization

Uncertain localization can be approximated by Gaussian distribution. I consider the influence of uncertain localization on safety constraints.

Uncertain Perception & Prediction

Path-time diagram

Predicted motion by using IDM on path-time diagram. The grey filled areas represent the regions that lie out of the reachability of the vehicle. Associated uncertainty to prediction. The distribution is truncated at the begin of the intersection.

Limited Visibility

Path-time diagram

For various sensor ranges (30 m − 110 m) the speed profile along the path of an intersection scenario. The vertical dashed red line corresponds to the intersection point.


One way to consider the uncertainties associated with motion planning is to use the POMDP framework, which encodes uncertain and incomplete knowledge not in single states, but by beliefs over all possible states. By optimizing over a sequence of actions and observations, they consider a very large number of possible future outcomes. This comes at cost of high computational complexity. I am doing research to solve the motion planning problem for automated driving with POMDPs efficiently.

Publications on this topic

Name Material
Ömer Sahin Tas, Christoph Stiller. Limited Visibility and Uncertainty Aware Motion Planning for Automated Driving. In Proc. IEEE Intell. Veh. Symp., Changshu, China, June 2018.