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