Perceptual navigation strategy: a unified approach to interception of ground balls and fly balls

In previous work, we demonstrated the feasibility of perceptual navigation algorithms used to intercept fly balls. In this paper we expand the optical acceleration cancellation heuristic to also intercept ground balls. We used computer simulations and experiments with mobile robots with various ball trajectories and different initial positions of the fielder to test our new model. A new robotic system with improved vision and faster processing was developed for experimentally intercepting ground balls. The results support the generality of viewer based interception heuristics for both fly balls and ground balls. 1.Introduction Human based algorithms to intercept fly balls have been research and studied. One theory suggests the path taken by a fielder is based on spatiotemporal relationships between the ball in space and the fielder on the ground. This strategy, called the optical acceleration cancellation (OAC) model, proposed that the fielder runs to maintain a constant increase in the tangent of the optical angle (gaze angle) while maintaining lateral alignment with the ball in order to intercept it. The same principle can be applied to intercept ground balls except that there is a constant decrease in the tangent of the optical angle measured from the horizon. Experimentally, enhancements have been made to speed-up the image processing. Real time image processing requires tremendous processing power on the host computer in the form of clock speed of the processor and the memory available. An image processing program, Digital Video Robot (DVRobot) was developed to process images very quickly. The camera and the computer communicate using the IEEE-1394 protocol. 2.Literature Review Chapman[1] in 1968 proposed that if α is the angle of gaze from a stationary fielder to a ball then the acceleration of tan( ) α is zero if the fielder is standing at the exact place where the ball will land. A fielder who starts from a place other than where the ball will land will eventually intercept the ball if he runs at a velocity such that the rate of change of tanα is maintained to be a constant. Oudejans and Michaels[2, 3] showed that the optical height (position of the ball on an imaginary plane located a fixed distance away from the fielder) increases at a fairly constant rate until just before the catch. This result was in agreement with Chapman’s findings. McLeod and Diennes[4, 5] filmed skilled fielders as they moved forward or backward to catch balls projected at them. They found that 2 2 (tan ) d d t α was maintained close to zero throughout the catching. We propose to develop a unified approach to intercept ground balls and fly balls. Support for the hypothesis that the human visual system uses angular declination is provided by the experiments of Ooi [6]. They found that observers significantly underestimated distances when they were blindfolded and asked to walk up to a target they previewed with a pair of base-up prisms. Thus they confirmed that when angular declination was increased, the observers underestimated distance. After adapting to the base-up prisms however, the observers over estimated distances on prism removal. The conclusion that over-estimation of distance as an after effect of prism adaptation was due to lowered perceived eye level which reduced the objects angular declination below the horizon. Their work was based on the assumption that visual Proceedings of the 2003 IEEE International Conference on Robotics & Automation Taipei, Taiwan, September 14-19, 2003 0-7803-7736-2/03/$17.00 ©2003 IEEE 3461 systems use the horizontal eye level as a reference for computing the angle of declination. In robotics various algorithms have been proposed and tested to track objects in 3D space. One of the methods proposed by Schulz[7] uses a sample based data association filter to track a moving object with a robot. In one of their experiments the robot was able to track and generate trajectories of three people moving in a passage and it was able to follow one of these people. Their approach used probabilistic methods to deal with a varying number of objects. Borgstadt [8], in another implementation of the OAC algorithm on mobile robots, collected acceleration data from the image, but this data was very noisy. In our previous work [9-12], we performed experiments with robots and computer simulations of perceptual navigation strategies using the OAC and the Linear Optical Trajectory (LOT) algorithms to intercept fly balls. We described active and passive models of the strategies based on the motion of the camera. 3.Mathematical Modeling and Simulation Figure 1.When the fielder first looks at the ball, the coordinate frame is rotated by an angle θ . This gives the new ' x , ' y axis. The original OAC strategy requires that the rate of change of the tangent of the optical angle to increase at a constant rate above the horizon. With ground balls, i.e. objects below the horizon (‘eye level’), the same principle is applied but with α being measured from the eye level downward. Thus when α is zero degrees the fielder is looking straight ahead and when α is close to -90 degrees, the fielder is looking vertically down. Ooi [6] proposed that objects are at infinite distance when 0 α = degrees and are extremely close when 90 α = − degrees. For simulations in world coordinates and to simplify the calculations, the coordinate frame is rotated by an angle θ based on the initial position of the fielder relative to the ball. For the purpose of modeling, the robot is assumed to be an omnidirectional robot. No skidding constraints are imposed. See Figure 1.