Obstacle Avoidance
3.2 Implementation
The PLIR traverses a power line with both grippers attached to the line. If an obstacle is detected, the PLIR must perform an obstacle avoidance manoeuvre in order to get around it and continue along the line. This requires each gripper to be removed from the line and reattached in turn to get around the obstacle. However, autonomous waypoint selection does not consider the actual detachment and reattachment procedures of the grippers for the time being. Due to the simplified robot representation as a set of points and lines, the grippers simply leave and join the power line as needed.
Although the PLIR has motorised wheels (rollers) attached to each gripper that allow the robot to traverse a power line, they are not used during obstacle avoidance manoeuvres at this stage. This is in order to simplify the problem at hand. The autonomous waypoint selection system creates obstacle avoidance trajectories based purely on the robot’s ability to reach around an obstacle. In the case of “long” obstacles, the AABB description length (along the power line’s z-axis) could be shortened if the robot is driven forwards during the obstacle avoidance manoeuvre.
For the creation of each gripper trajectory, it is assumed that a high-level image processing system has provided the necessary information about the obstacle in the way. It is also assumed that the PLIR is instructed by the image processing system to stop an appropriate distance from the obstacle. Once the PLIR has stopped, an obstacle avoidance manoeuvre needs to be carried out so that the PLIR can get around it.
Figure 3.6: Figure showing the positions of the minimum and maximum boundaries of the AABB.
3.2.1 Waypoint selection
In order for a trajectory to be created, a set of waypoints is required as discussed in Section 2.3. For obstacles on a power line segment (such as dampers), the initial and final waypoints are assumed to be collinear on the power line’s z-axis. Furthermore, the power line segment that is considered over the range of the manoeuvre is assumed to be straight. This assumption is supported by Figure 3.4 where the line appears to be straight over that particular segment.
Once the robot has stopped before the obstacle, the positions at which the front and rear gripper have come to rest are used as their initial waypoints. The simulated model has the robot come to rest 3 cm from the start of the obstacle representation. The rear gripper is 15 cm behind that since that is the closest the two grippers can be to one another in order to provide maximum reach. The final waypoint for the front gripper must be 18 cm past the far side of the obstacle representation, allowing the rear gripper to re-attach 3 cm clear of the far side of the obstacle representation. These measurements have been set experimentally and are found to yield desirable trajectories. As an example, the initial and final waypoint locations for the vibration damper representation are shown in Figure 3.7.
For obstacles that require initial and final waypoints that are not collinear (in the case of a jumper, shown in Chapter 6), the image processing system has to provide the initial and final waypoints explicitly (beyond the scope of this dissertation). Once the initial and final waypoints have been set, intermediate waypoints must be chosen so that a collision-free path can be created around the obstacle. There are many different paths that a gripper can take to get around a given obstacle. It is preferable to choose the path that requires the least amount of electric charge for the manoeuvre due to power supply constraints. However, since there is no analytical method for finding such a path due to the highly coupled nature of the robot’s forward dynamics solution, it is sensible to find the “shortest distance” path and optimise the trajectory time instead. It is observed in simulation experiments that this will be close to the performance of the “minimum charge” path in terms of charge consumption.
The shortest path in the 3D workspace graph around an obstacle from a start node to an end node can be found using the Lazy Theta* algorithm (Nashet al., 2010). The Lazy Theta* algorithm
Figure 3.7: Figure showing the top view of the initial and final waypoints in the case of a vibration damper.
is based on the popular A* algorithm used for finding shortest paths between two graph nodes comprising of graph edges. Being restricted to graph edges is not desirable for the PLIR application, since a path confined to graph edges may not actually be the shortest path. A* finds the shortest path between two nodes by propagating path information along graph edges, and then linking the edges between the two nodes that result in the shortest path.
Unlike A*, Lazy Theta* does not restrict the path itself to graph edges, it allows path segments to join any two nodes that can make up part of the shortest distance path as long as they have line-of-sight of each other (no obstacles between them). The initial and final waypoints for an obstacle avoidance manoeuvre will be selected by the high-level automation system. The nodes generated by the Lazy Theta* algorithm are used as the intermediate waypoints between the initial and final waypoints, all of which are used to create the trajectory. A comparison between A* and Lazy Theta* is given in Figure 3.8. The comparison is made in only two dimensions here for the purpose of clarity.
The path obtained by the A* algorithm is not the shortest path, whereas the Lazy Theta* solution is. The vertices used for the shortest path solution (marked by the “+”s in Figure 3.8) can be used as the waypoints from which obstacle avoidance trajectories can be created. The full description of the Lazy Theta* algorithm is given in Nashet al.(2010).
The line-of-sight checks for the PLIR application are performed using an algorithm from Ericson (2005), Chapter 5: “Basic Primitive Tests”. The algorithm checks for an intersection between a line segment and an AABB. If no intersection occurs, the two points that describe the line segment have line-of-sight of one another. This line-of-sight algorithm is also used in Section 3.2.2 to detect collisions between the robot and the obstacles.
The selection of waypoints is restricted to the subset of the robot’s workspace in the quadrant along the z-axis between the negative x-axis and the positive y-axis as shown in Figure 3.9. This admissible region is described relative to the gripper’s coordinate frame. The restriction is due to the physical configuration of the robot and the method used for finding a collision-free path. Since the path is first found for the gripper only without considering other robot parts, crossing from one side of the line to the other or attempting to pass over an obstacle brings the robot parts closer to the obstacle instead of moving away from it, and increases the likelihood of a collision.
Once the waypoints have been generated, a trajectory is created with the waypoints using an interpolating fifth order B-spline. The reason an interpolating spline is chosen instead of an approximating one is because the trajectory must not enter the obstacle boundaries at any point along its path. Since the waypoints exist on the obstacle boundaries themselves, approximation could result in a collision with the obstacle as discussed in Section 2.3.2. The gripper trajectory is
Figure 3.8: Figure showing the shortest path result of the A* algorithm (left) vs the Lazy Theta*
algorithm (right).
checked for collisions between the robot and the obstacle as discussed in Section 3.2.2. If the front gripper trajectory is free from collisions, it is accepted and the entire trajectory creation procedure is carried out for the rear gripper.
3.2.2 Collision detection
Once obstacle avoidance trajectories have been generated, they are executed in a simulated environment to check for collisions between the obstacle and the robot body. Obstacle avoidance trajectories created for each of the grippers may be collision-free for the gripper itself, but not necessarily for the entire robot. Each joint actuator trajectory consists of a number of discrete gripper positions, and the robot configuration at each of these positions calculated at time steps of T = 15 ms as discussed in Section 2.4. It is necessary for the trajectory to be checked for collisions between the robot body and the obstacle at all of these configurations.
The collision checks are simple to perform due to the basic representation of the robot as mentioned at the beginning of the chapter. Since each of the robot parts are represented by a line segment, collisions can be investigated using the algorithm from Ericson (2005) that was used to perform line-of-sight checks. If any of the line segments making up the robot intersect an obstacle, a collision has occurred. If a collision is detected, the trajectory being tested is rejected. Depending on which part of the robot collides with the obstacle and where the collision occurs, the original AABB description must be enlarged to yield a new AABB description. With this, a new trajectory is formed that must then be checked against the original AABB description for collisions. If the new trajectory is collision free, it is used to command the robot. If the new trajectory is not viable, the robot will have to be assisted by a human operator at this point in the development stage, using a ground station computer (discussed in Chapter 5).
Figure 3.9: Figure showing the admissible waypoint insertion region in the robot’s workspace.