Minimum-Energy Motion Planning for Differential-Driven Wheeled Mobile Robots
Chong Hui, Byung Kook · InTech eBooks · 2008
In this book chapter, we derived the minimum-energy trajectory for WMR considering practical energy drawn from the batteries. First we investigated the minimum-energy translational trajectory generation moving along a straight line. Using the Pontryagin's Maximum Principle, the energy-optimal velocity profile that minimizes total energy drawn from the batteries is found to be a reasonable complex analytic form. The minimum-energy velocity profile is shown to depend on the ratio of the mechanical time constant and displacement time. Simluations show that minimum-energy control can give significant energy savings, up to 8% compared with loss-minmization control and up to 6% compared with the widely used trapezoidal velocity profile, minimizing the total energy drawn from the batteries. The experimental results also showed that the proposed minimum-energy control can save the battery energy up to 11% compared with lossminimization control. Since WMR also needs turning trajectory as well as translational trajectory to do useful actions, we also investigated the minimum-energy turning trajectory planning for WMR. To overcome nonholonomic and nonlinear properties of a WMR, we divided our trajectory into three sections. The first is RS, which is focused on the rotational motion with the required turning angle, and the others are TSB and TSA, which are adjoining procedures focused on translational motion. Energy optimal trajectory for each section was obtained using the Pontryagin's Maximum Principle. To combine three sections and find the minimum-energy trajectory, since there is no closed-form solution combining three solutions, we suggested an iterative search method with quintuple loops based on observations of the cost function. Since iterative search is composed of quintuple loops and there are many iterations loops to calculate robot's position due to its nonholonomic property, we implemented the algorithm in C language and simulations took several hours using a PC with Intel Core2 Duo 2.13GHz. Simulation results showed that the minimum-energy turning trajectory can save the battery energy up to 8% compared with loss-minimization turning trajectory. The experimental results also revealed that the minimum-energy turning trajectory can save up to 9% of the energy drawn from the batteries compared with loss-minimization turning trajectory. As a further works, it remains a problem to solve about on-line trajectory planning for the overall real-time control of WMR. Also it is necessary to design a trajectory tracking controller reducing velocity tracking and posture errors for more accurate motion control for actual robots.