Hierarchical control architecture operates based on the sense-plan-act robot control methodology [17]. Initially, information about the surrounding environment of the robot is gathered through the sensors, then a motion plan of the next gait cycle is calculated in a goal oriented manner. Finally, the planned action is undertaken through actuators. Then the same procedure is repeated until the goal of the given task is achieved [17]. Figure 4.1 shows the block diagram of the hierarchical control architecture that is implemented in the hexapod robot. It is assumed that the terrain features are provided before the execution of the simulation.

Figure 4.1 Hierarchical Control Architecture

For a given start point, A and a goal point, B, the shortest distance may be calculated using a map-based planning method. Note that, the shortest distance may have a higher movement cost, i.e. there might be a longer path with fewer obstacles and easier to navigate. In order to designate whether or not this is the case, the cost map of the terrain needs to be taken into account which indicates how easy the terrain is to navigate over [6]. In this report, the shortest path is assumed to be the one with the lowest movement cost.

Figure 4.2-a Uneven terrain and the 2D representation of terrain, adapted from [15]

Figure 4.2-a
shows an uneven terrain where the regions that are higher than the reachable
workspace of the robot leg, are represented as obstacles in the 2D grid that is
shown on Figure 4.2-b. For example, Figure 4.3 shows a terrain height where the
robot is capable of stepping over, hence in the 2D grid representation, also
referred as occupancy grid, of this region is not an obstacle.

Figure 4.3 Collision map of a foot trajectory over an obstacle, adapted from [28]

The occupancy grid framework provides information about terrain regarding to the free spaces and obstacles where each grid is roughly equal to the size of the robot. [29] For the computation, the occupancy grid is represented as a multidimensional matrix where 0 denotes free space, Qfree, and 1 denotes obstacle, Qobs [14].

The path planning algorithm, A* (star), that was implemented to compute the body path, runs in discrete space, however the real‐world is continuous hence the map needs to be discretised which is done by using an approximate cell decomposition method, trapezoidal decomposition [30]. Figure 4.4 shows the occupancy grid that was used in the MapleSim simulations. Using the trapezoidal decomposition approach, it can be decomposed into 7 cells. The idea is to extend a vertical line in Qfree until it touches either a Qobs or reaches the borders of occupancy grid [31] [32]. There is a harder-to-compute decomposition method, named as exact cell decomposition, which covers the exact shape of Qobs using convex polygons, i.e. this method produces cells with irregular boundaries. However, since all the obstacles are chosen to be rectangular, trapezoidal decomposition is sufficient enough in this particular example.

Figure 4.4 Occupancy Grid Representation

Figure 4.5 Adjacency Map of the Occupancy Grid.

Then, an adjacency map is generated where each cell is represented as a node and the adjacent cells are connected with a line, shown in Figure 4.5. The adjacency map can be expressed in matrix form, where the adjacent cells are represented as 1 and the rest as 0, given by Equation 28.

A* (star) path planning algorithm determines the cost of the 8 surrounding nodes by using Equation 28,

where G is the distance from the start node and H is the estimated distance from the end node using heuristics [30]. G and H are calculated ignoring the obstacles, where the vertical and horizontal movements are counted as increments of 1 whereas the diagonal motions are counted in increments of **√**2. Table 3-1 shows an example of how G and H were calculated for Nodes A, B, and C that are shown on Figure 4.6. The nodes with the lowest...

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