IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART A: SYSTEMS AND HUMANS 1 Two Mitigation Strategies for Motion System Limits in Driving and Flight Simulators Chris W. Schwarz, Member, IEEE Abstract—Limited workspace is a challenge for all motion- based simulators, whether they are large excursion systems like the National Advanced Driving Simulator or smaller simulators utilizing only Stewart Platforms. Two approaches for addressing this challenge are nonlinear washout scaling and software dis- placement limiting. This paper presents new algorithms devel- oped for these approaches. The nonlinear scaling method uses the cubic Hermite interpolation polynomial to smooth the cor- ner in the scaled output at the limit. A software displacement limiting method that generates control signals in the table frame of reference is introduced. As a result, unwanted acceleration artifacts caused by unbalanced limiting of actuators are avoided. The methods are described, and offline simulation results using the new displacement limiting method are presented. Index Terms—Displacement control, limiting, motion compen- sation, motion control. I. I NTRODUCTION D RIVING and flight simulators are commonly used today for research and training. All motion-based simulators have in common that they attempt to reproduce vehicle dynam- ics within a very limited workspace. Thus, onset accelerations can be reproduced quite accurately, but sustained ones cannot. Motion limits on position, velocity, and acceleration are typi- cally enforced to prevent damage to the machine. Preferably, the motion drive algorithm (MDA), i.e., washout never lets the motion base reach a limit; however, it does happen in practice. A software-limiting scheme can mitigate these occurrences by gently slowing the offending actuator down and holding it under the stroke limit. Actuator limiting can produce unacceptable false motion cues to the driver. As a result, simulator operators often have to be extremely conservative when setting the MDA parameters so that actuator limiting is never encountered. The goal of the methods described herein is to provide ways of mitigating the adverse effects of hitting motion limits. If this can be done successfully, it may allow the simulator operator to relax their constraints on the motion, for example, by opening up the MDA to provide larger onset cues. As a general rule, motion limits should still be avoided; however, an increase in performance could be realized if the operator was able to tune the system for the average driver/pilot rather than the Manuscript received October 27, 2005; revised September 4, 2006. This paper was recommended by Associate Editor L. Rothrock. The author is with the National Advanced Driving Simulator, Iowa City, IA 52242 USA (e-mail: cschwarz@nads-sc.uiowa.edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSMCA.2007.897590 worst case. Then, when the worst case is realized, the resulting motion commands will be dealt with in ways that do not cause unacceptable false cues. The simplest method of constraining the motion commands in the MDA block is to provide scaling factors for each degree of freedom (DOF) and clip the signal if a specified acceleration or velocity limit is reached [1], [3]. Encountering this type of limit will cause a sharp jerk and wipe out all cues above the limit. A variation on this approach is to replace the clipping limit with a linear scale region of reduced slope so that the scaled output grows more slowly than the input [3]. A newer polynomial-based nonlinear scaling method was introduced in [3]. The third-degree polynomial used there is similar to the Hermite approach, but the parameter set is more complicated, and there are no guidelines for wisely selecting the parameters of the polynomial. In the worst case, the scaled output can expe- rience local minima when the input is monotonic. The proposed nonlinear scaling method addresses these shortcomings. The second strategy specifically regards the workspace limits of the Stewart Platform. These occur if the stroke limit of an actuator is reached, if two actuator legs collide, or if a joint reaches a mechanical limit. A well-designed hexapod for simulator application will reach the first type of limit before ever reaching the next two. A review of Stewart Platforms was compiled in [5]. An actuator-limiting method is described in [2] for the Uni- versity of Toronto Institute for Aerospace Studies (UTIAS) flight simulator. The method computes a distance from the actuator limit at which deceleration must begin to remain below a specified level. The actuator comes to a stop as the virtual ac- tuator position is tracked beyond the limit and back into the al- lowable region. Then, the actuator accelerates and again tracks the position command. This algorithm effectively softens an encounter with a limit but may still create a noticeable false cue. Rubio et al. proposed a controller that avoids workspace limits and singularities with the use of virtual springs [4]. Theirs is a force–force controller and requires the consideration of the Stewart Platform dynamics. As well, control occurs completely in actuator space and therefore could still produce artifacts in the simulator reference frame. The kinematic mapping from simulator positions to actuator positions is quite simple to do; however, the inverse problem is more complex, which requires the solution to be either a high- order polynomial or several simultaneous nonlinear equations. Dieudonne et al. introduced an iterative method to solve the inverse kinematic equations in real time [6]. We have chosen here to avoid the standard iterative technique in favor of using 1083-4427/$25.00 © 2007 IEEE