Motion Planning for Camera Movements in Virtual Environments

Authors: D. Nieuwenhuisen, M. OvermarsPresenter: David Camarillo

Introduction Manual Navigation in VE

Difficult to do efficiently Can lead to disorientation

and motion sickness Prevents operator from

focusing on higher level task Automatic Navigation

User only need specify goal position

Smooth path generated according to cinematography

Theory of Cinematography Distance to

prevent fear of collision

Horizon maintained to prevent “drunk” view

Lower speed in sharp turns

Maximize camera speed to a bound

Visual cues as to future directions

Strategy1. Create PRM based only on position (pre-

processed)2. On query, add start (s) and goal (g) as

nodes3. Find path in roadmap with minimum time4. Smooth path (continuous)5. Compute time-trajectory (continuous)6. Shorten path by randomly connecting

nodes7. Remove near nodes for fewer segments8. Smooth viewing direction

Create Roadmap (PRM)

Nodes are spheres to maintain halo

Create random nodes Check for path to n

nearest nodes Must have collision

free cylinder On query, connect s

and g as any other node

Find Path in Roadmap with Minimum Time

Shortest distance has sharp turns that will take more time

Cost function for an edge:

Use Dijkstra’s shortest path algorithm

Time O(n log(n))

)()',()( eleeped

Smooth Path Make 1st order continuous (spatial derivative

defined) Add circular arcs A collision free arc will always exist Binary search to find largest collision free arc Collision checking of arc computationally

expensive

Smooth Path

Compute Time-Trajectory

Max position speed should depend on curvature of path

Experimentally determined smax(r)

Want continuous trajectory, s(r) Use max acceleration and

deceleration for speed graph Backtrack deceleration to

guarantee bottom corner Accelerate maximally up to

threshold or new edge

Shorten Path We now have continuous path from PRM Since coarse map, not shortest path Test shorter paths

1) Connect two random points on path2) If collision free, add default circle arcs3) Calculate speed diagram and compare4) If improved, keep and calculate arc radii

Results in too many edges (many speed changes) Remove close nodes

Smooth Viewing Direction Want viewing direction 1st

order continuous Time derivative defined

Look at W(t+td) Continuity guaranteed Distance ahead depends on

depends on speed Sharp turns look at nearer point

Implementation Movieshttp://robotics.stanford.edu/~latombe/cs326/2004/class16/class16.htm

Video 1Video 2

Future Research Following human paths Third-person view with partially

known trajectory Must account for obstacle occlusion