Planning Biped Navigation Strategies in Complex EnvironmentsJiaan Zeng

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.

Problem

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.

Solution

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.

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).

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.

Model

Transitions

Model

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

Model

Evaluation Function: L(Q) Location Metrics

L(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

Model

Location Metrics ― Plane Fitting

Model

Evaluation Function: S(Q, T, Qc)

Evaluation Function: R(Q, Qg)

Model

BFS (Best First) f=g= L(Q)+S(Q, T, Qc) A* f=g+h=L(Q)+S(Q, T, Qc)+ R(Q,

Qg)

Algorithms

Environment Simulation

Physical Robot

Empirical Results

Various Types of Terrain

Empirical Results

Distance to Goal

Empirical Results

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

Empirical Results

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

Empirical Results

TransitionsComparison of the output of BFS versus A* on environments with local minima.

Empirical Results

WeightsCarefully choosing the weights for the different metrics is very important for the runtime of the algorithm

Empirical Results

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

Empirical Results