Time optimal trajectory planning for formation driving of Mars
rovers

Abstract: Currently the research on Mars exploration rovers is under much
investigation. The motivation of this thesis work stems from the blind
formation driving of future MER missions. The Mars rover prototype in our
laboratory is the indoor MERLIN car-like robot. The main goal of this thesis
is time optimal trajectory planning for the leader robot in formation group.
Several planning methods have been investigated and the proposed trajectory
planning method has been verified with simulative and experimental tests on
real hardware.

Firstly, one standard path planning method, Visibility Graph Method, and one
newly developed method, Ferguson Cubic Splines Method are employed for
distance optimal path planning under kinematic constraints of car-like robot.
User interfaces are built and both methods are simulated in Matlab. The
comparison between them shows the advantage of Cubic Splines Method.

Secondly, the time optimal trajectory planning with cubic splines is studied,
in which both kinematic constraints and dynamic constraints are considered.
The velocity profile under these constraints is established in light of path
curvature and the distance from the path to the nearest obstacle. The key of
trajectory planning is how to obtain the feasible velocity profile that
satisfies acceleration limit. An efficient algorithm is developed to solve
this problem and is verified with simulation. The main advantage of the
planned trajectory is the continuous velocity profile and steering angle
profile, which satisfy both kinematic and dynamic constraints.

Finally, the proposed trajectory planning algorithm is verified through
driving experiments with the indoor MERLIN robot. A PID controller on speed
is designed for stable outputs. The steering angle is calibrated and a
real-time measuring method for steering angle is tested. Example trajectories
with time-variant curvature and velocity profile are implemented.