Planning Biped Navigation Strategies in Complex Environments

1. Planning Biped Navigation Strategies in Complex Environments Jiaan Zeng

2. Problem • Plan goal-directed footstep navigation strategies for biped robots through obstacle-filled environments and uneven ground. • Conventional 2D planning algorithms designed for wheeled robots would be unable to find a solution.

3. Solution • This paper models the problem as a standard search problem. • The planner uses an A* search to generate a sequence of footstep locations to reach a given goal state.

4. Model • InputA map representing the terrain to plan over, an initial and goal state. • OutputIf a path is found the planner returns the solution as an ordered list of the footsteps that should be taken to reach the goal.

5. Model • State Space The state variables x, y, and θ denote the relative position and orientation of the footstep, and the binary variable s ∈ {R,L} denotes which foot is currently the support foot (right or left).

6. Model • Successor Function(State Transition) • An upper and lower allowable height change HCupper and HClower, and an obstacle clearance value, clearance, representing the largest obstacle that the transition can step over.

7. Model • Transitions

8. Model • Evaluation Function (State Evaluation) f = L(Q)+S(Q, T, Qc)+R(Q, Qg)

9. Model • Evaluation Function: L(Q) • Location MetricsL(Q) =∑ƜiMi (i=1, …, 5) • M1 how slope the plane is • M2 how roughness the plane is • M3 how stability the plane is • M4 the largest bump • M5 how safety the plane is

10. Model • Location Metrics ― Plane Fitting

11. Model • Evaluation Function: S(Q, T, Qc) • Evaluation Function: R(Q, Qg)

12. Algorithms • BFS (Best First) f=g= L(Q)+S(Q, T, Qc) • A* f=g+h=L(Q)+S(Q, T, Qc)+ R(Q, Qg)

13. Empirical Results • Environment • Simulation • Physical Robot

14. Empirical Results • Various Types of Terrain

15. Empirical Results • Distance to Goal

16. Empirical Results • TransitionsPerformance comparison of BFS (left) and A* (right) for different sets of available footstep transitions.

17. Empirical Results • TransitionsPerformance comparison of A* (left) and BFS (right) for increasing numbers of stairs along the path from the initial to goal state.

18. Empirical Results • TransitionsComparison of the output of BFS versus A* on environments with local minima.

19. Empirical Results • WeightsCarefully choosing the weights for the different metrics is very important for the runtime of the algorithm

20. Empirical Results • Online Footstep PlanningVision Processing steps. Raw camera images and resulting 3D Depthmap; Mesh model, planar surface identification, and final walking area map.