Thomas M. Howard Alonzo Kelly Robotics Institute Carnegie Mellon University Pittsburgh, PA 15213-3890, USA {thoward,alonzo}@ri.cmu.edu http://www.ri.cmu.edu/people/ {howard_thomas,kelly_alonzo}.html Optimal Rough Terrain Trajectory Generation for Wheeled Mobile Robots Abstract An algorithm is presented for wheeled mobile robot trajectory gen- eration that achieves a high degree of generality and efficiency. The generality derives from numerical linearization and inversion of for- ward models of propulsion, suspension, and motion for any type of vehicle. Efficiency is achieved by using fast numerical optimization techniques and effective initial guesses for the vehicle controls pa- rameters. This approach can accommodate such effects as rough terrain, vehicle dynamics, models of wheel-terrain interaction, and other effects of interest. It can accommodate boundary and internal constraints while optimizing an objective function that might, for ex- ample, involve such criteria as obstacle avoidance, cost, risk, time, or energy consumption in any combination. The algorithm is efficient enough to use in real time due to its use of nonlinear programming techniques that involve searching the space of parameterized vehicle controls.Applications of the presented methods are demonstrated for planetary rovers. KEY WORDS—mobile robots, trajectory generation, rough terrain, constrained optimization, optimal control, path planning 1. Introduction In order to operate competently in any environment, a mobile robot must understand the effects of its own dynamics and of its interactions with the terrain. It is therefore natural to incorporate models of these effects in a trajectory generator that determines the controls necessary to achieve a prescribed motion. Trajectory generation is the problem of determining a fea- sible motion (or a set of feasible motions) that will permit a vehicle to move from an initial state to a final state given some model of the associated dynamics. While this two-point The International Journal of Robotics Research Vol. 26, No. 2, February 2007, pp. 141-166 DOI: 10.1177/0278364906075328 ©2007 SAGE Publications Fig. 1. Motion planning on rough terrain. For competent navigation in challenging environments, the terrain shape must be considered in the generation of continuous motion trajectories. The presented trajectory generation algorithm generates motion plans that account for arbitrary terrain shape, vehicle dynamics models, and wheel/terrain interac- tion models by linearizing and inverting forward models. boundary value problem is classical and well studied, it re- mains quite complex to solve adequately in practice. In order to generate a smooth, continuous path on flat terrain (which satisfies an arbitrary number of constraints involving position, heading, linear and angular velocities, and/or curvature), a nonlinear differential equation must be solved. The addition of rough terrain to the problem further compli- cates matters by coupling these nonlinear equations of motion. Numerical methods, such as the ones presented in this arti- cle, are required to solve such problems for arbitrary terrain due either to its typically sampled representation, the non- linearities of the models, or the nonexistence of closed-form integrals of the dynamics. 141 at University of Sydney on October 12, 2009 http://ijr.sagepub.com Downloaded from