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Dynamics and control of robotic systems is a difficult problem because of the large rigid body displacements resulting in nonlinear equations. In particular, flexibility in the links and joints have been of interest to us. We have also been working on hyper-redundant systems with a "large" degree of redundancy. These could result in potentially very unusual and useful configurations such as an "artificial" snake. Some of this work has been carried out in collaboration with Dr. Hashem Ashrafiuon. Recently, Villanova has received a large grant from DARPA for an inter-disciplinary project related to micro-miniature devices and their application to micro-robotics.

Research Topics in Robotics

Obstacle Avoidance

The issue of path planning and obstacle avoidance in a known environment has been addressed by many researchers. The proposed strategies are applicable to both mobile robots and manipulators and can be divided into two broad classes: global and local. The global techniques are guaranteed to give a free path if such a path exists. However, their computation time increases exponentially as the degree of freedom of the robot increase. This computational complexity limits their use for real-time obstacle avoidance to only very simple cases. Local strategies are typically based on the artificial potential function approach and can be implemented either in task space or in configuration space. In the artificial potential approach, the obstacles to be avoided are represented by repulsive artificial potential, and the goal is represented by an attractive potential so that a robot reaches the goal without colliding with obstacles. The approach is computationally much less expensive than the global approach and therefore is suited for real-time implementation. The artificial potential approach, however, has been limited due to existence of local minima and its inability to deal with arbitrarily shaped obstacles. But artificial potential functions, based on harmonic functions, overcome the limitations of the potential approach and are proved to be the most computationally efficient approach. The two-dimensional version of potential approach based on harmonic potential fields is applicable to both car-like, and Hilare-type mobile robots. We coded a path planar engine based on the 2D version of this theory for our car-like and Hilare-type mobile robot prototypes. We also successfully implemented this theory on mobile platforms.

Obstacle Avoidance with kinematic constraints

The above approach is based on the concept of a point robot. The real robot, however, is subject to kinematic constraints as discussed earlier. Hence, we adapted the potential approach to the problem of obstacle avoidance of a real car-like robot with the objective of being able to recover the motion along a pre-planned path when the robot encounters an obstacle. We looked at simple paths such as circular and sinusoidal ones. In addition, since a general arbitrary function can be expressed in the form of a Taylor series, which is a polynomial series, we automated the path planning process for a polynomial path. The figure shows the ability of our mobile robot to follow a polynomial path. In addition, the figure shows the obstacle avoidance (with all kinematic constraints being satisfied) on a circular path. Details on optimal path planning to conserve energy or time (with dynamical constraints) can be found in Masoud Feghhi's Master's thesis.

Effect of Dynamics

From a detailed analytical investigation, we found that the dynamical effects that are almost always ignored by past researchers are indeed very important and can introduce large errors in the path planning that was discussed above. An example of such an error pursuing a simple circular path is shown in the figure. Note that these errors would increase continuously as the robot repeats the circular path to a point when it would be completely off the intended path. We performed several physical experiments on the indoor platforms to investigate the effect of mass, radius of path, location of center of mass (that would change when an arm is mounted on the mobile platform) on these errors.

Three Dimensional Terrain Planning

The real world is three-dimensional, a fact that is very important to consider when we are dealing with small platforms in an outdoor setting. Hence we looked at the problem of modeling and simulation of wheeled mobile robots moving on an uneven terrain. To this end, we have proposed and implemented an approach based on modern geometric modeling tools to represent and obtain properties of a surface from a given set of measured elevation data. We have also developed equations of contact (non-holonomic constraints) for a single disk moving in contact with such surfaces. We have also attempted to develop constraint equations for a two-wheeled vehicle. This works needs to be carried to its natural conclusion by extending to 4 wheeled car like vehicles and performing simulations for such 4 wheeled vehicles on actual measured terrain data. In addition to the kinematics of wheeled mobile robots as described in our technical report, future research will also include static stability, dynamics and control issues. Motion planning can then be attempted for four wheeled car-like vehicles moving over uneven terrain.

Reduction in Task Space Of Mobile Robot

Biasing, once regarded as "cheating" in machine learning community is now understood and accepted as a necessary part of learning. However, despite its wide acceptance and recognition, biasing has not been studied extensively as a separate research issue, except in a few instances, where an attempt is made to shed light on the relationship between the quality of bias and learning trials. So far, the general view held in biasing a learning system is to look for a bias that maximally collapses the search space. It is well known, however, that reckless reduction of the search space often leads to sub-optimal learning. Regardless of the final level of optimality, we challenged this broadly accepted biasing scheme from the point of view of accelerating the learning process itself. Is a large search space a definitive indication of slow learning? We have challenged this broadly accepted view by presenting a variety of grid based robot learning scenarios. All experiments clearly show that a bias that is derived from the unique characteristic of the task results in a better learning behavior than a bias that reduces the search space aggressively. The algorithms we derived are expected to help robotic devices develop a greater degree of autonomy in being able to navigate around obstacles and to home in on a target. Experiments

The obstacle avoidance theory for mobile platforms was programmed on the EyeBot micro-controller that controls the car-like mobile robot. In the first version of the control software, it is assumed that the geometry and location of the obstacles are known. Therefore, the corresponding data is predefined in the controller software. The current position and orientation of the platform and the desired goal position is given to the controller software as inputs. The controller software generates a hypothetical potential field based on the geometry and location of the obstacles and the input data, and uses the potential field to plan a path from the current position of the platform to the goal position. Then, it drives the robot on the computed path and stops the robot when it has reached the goal position. Some experiments with different configuration of obstacles were carried out. Experiments show that if the distances between the obstacles are reasonable compared to the size of the robot, the robot avoids obstacles successfully and reaches its goal position with an acceptable accuracy.

Car-like robot avoiding known obstacles

In the next step, a simple vision system based on a rotating infrared sensor was added to the robot. An image processing routine was also programmed on the robots' controller. The infrared sensor rotates 180 degrees and scans the environment. The image processing routine processes the raw scanned data and approximates the location and geometry of the obstacles. Based on the approximation and current and goal positions of the robot, the controller software plans a path and drives the robot as far as the max view distance of the infrared. The scanning and path planning are repeated until the robot is at goal. After adding the vision system and image processing routine, the robot is able to detect the obstacles and avoid them autonomously, at the cost of more computation time. Furthermore, since the obstacles' geometry is approximated, the controller software fails to avoid obstacles where they are set up too close.