Obstacle Avoidance and Motion Planning are both necessary components for any robotic task. Obstacle Avoidance refers to planning collision-free trajectories for robotic systems while Motion Planning refers to planning smooth motions for robotic systems. Both of these are active research topics at the RRG as well as being prominent research topics at institutions around the world. This webpage will introduce our approach to these problems and provide links for further information.

Table of Contents

1. Approach - Describes the basic approach taken towards Motion Planning and Obstacle Avoidance
2. Research and Results - Provides a more in-depth discussion of the RRG's research in Motion Planning and Obstacle Avoidance
3. Simulations - Contains several video simulations showing Motion Planning and Obstacle Avoidance applications
4. Documents - Provides links to previous theses and dissertations on these research topics as well as several publications.

The overall goal of motion planning is to provide a smooth trajectory to improve performance by reducing wear on actuators as well as providing a more visually pleasing movement. In order to fully realize this goal, the dynamic and compliance effects of the system as a whole must be considered in the planning of the motion. This approach has been applied successfully to 1 and 2 DOF Cam systems by Tesar & Matthews [1]. This work shows that through the use of input synthesis (taking into account the dynamic outputs into the input) that the system shocks and distortions can be reduced. However, this is a much more daunting task for a high-DOF robotic manipulator[6]. Thus, current research is focusing on studying and evaluating spatial trajectories. The goal is this research is to understand how the underlying geometry and mathematics of spatial curves affect the motion planning problem.


II. OBSTACLE AVOIDANCE

The work in Obstacle Avoidance at the RRG deals primarily with using redundancies in a robot manipulator to avoid collisions in a workspace. This method takes advantage of the fact that in redundant systems there are an infinite number of joint positions that satisfy the same end-effector position. This is shown in Figure 1. The current implementation of Obstacle Avoidance at the RRG uses Performance Criteria to determine a joint position that avoids collisions. This involves perturbing some of the joint values to develop a set of possible solutions. These solutions are then ranked based on certain criteria, and the best solution is chosen. The RRG has already implemented over 10 criterion dealing with Obstacle Avoidance [4]. For more information on Performance Criteria and Decision Making, click here.

Figure 1. Self Motion Manifold

Motion Planning is a fairly new topic at the RRG and is in the early stages of development. Currently, research is focusing on generating and studying the geometry of spatial curves. This is only one small part of motion planning; however, it is important to build an understanding of the underlying mathematics of spatial curves. This research focuses on analyzing the mathematical properties of spatial curves such as curvature or torsion and building criteria based on these properties that can be used to evaluate and compare different path trajectories. Figure 2 shows a sample spatial curve with an attached Frenet frame. Another important aspect of this research is to further relate these curve properties and criteria to the input parameters of a robot manipulator. This is done using the kinematic influence coefficient model developed by Thomas and Tesar [1]. This model is generalized and can be used on a wide variety of systems ranging from complex hyper-redundant manipulators to simple planar systems. For example, the equation for the Normal vector in terms of input G and H functions is shown below.

Figure 2. Spatial Curve and Frenet Frame

These formulations provide valuable information on the relationships between curve properties and input demands. On top of this, these ouput criteria can be combined with input criteria (such as those for Obstacle Avoidance) in the same decision making framework.


II. OBSTACLE AVOIDANCE

As stated earlier, our approach to Obstacle Avoidance builds on the Decision Making framework implemented by the RRG. This involves using Performance Criteria to measure and compare the quality of various possible joint solution sets. These criteria are based either on maximizing the distance between the manipulator and an object or by mapping distances between the manipulator and the environmental obstacles to artificial torques or EEF forces on the manipulator. The performance criteria currently implemented at the RRG are as follows:

1. Smallest Minimum Distance: The smallest distance between the manipulator and the environment obstacles. It is calculated as follows:
   
   
2. Average Reciprocal Distance: The average of the reciprocal distances between the manipulator links and the environment obstacles. This is shown in the equation below:
   
3. Average Link Force: Distances between manipulator links and environment obstacles mapped to artificial forces acting on the links. This is calculated using the following equation:
   
4. Average Joint Torque: The artificial link forces used in average link force mapped to manipulator joint torques.
   
   
5. End Effector Wrench: The artificial joint torques used in average joint torque mapped to a combination of forces and torques acting on the manipulator end effector.

In order to model the manipulator and obstacles in the workspace, we use three basic shapes: spheres, cylispheres, and planes. These basic shapes allow for easy calculations of distances and can be combined to represent fairly complex objects. Figure 3 shows the 7 degree of freedom Mitsubishi PA10 modeled using cylispheres.