LP BASED GLOBAL MINIMIZATION OF PEAK BASE REACTION FORCE OF MANEUVERING ROBOTS Matthias Schmid * Department of Mechanical & Aerospace Engineering University at Buffalo, The State University of New York Amherst, NY 14260-4400 Lukas Ramrath † Department of Mechanical & Aerospace Engineering University at Buffalo, The State University of New York Amherst, NY 14260-4400 T. Singh ‡ Department of Mechanical & Aerospace Engineering University at Buffalo, The State University of New York Amherst, NY 14260-4400 ABSTRACT A method for computing the optimal control to min- imize a robot’s peak base reaction force, while avoiding obstacles, is presented. It contains the manipulator dynamics, initial and final conditions and obstacle con- straints. Using the assumption that minimal peak base reaction force control is equal to time-optimal con- trol, an iterative approach is used to find the path and control that globally minimizes the robots peak base reaction force. The conditions for optimality are derived and incorporated into an algorithm which uses linear programming to solve the given problem. Equa- tions describing the system dynamics and the obstacle position are mapped into the center of mass space, a convenient space for path planning. The method is demonstrated for a general maneuver in the center of mass space and for a two-link manipulator which in- cludes obstacle constraints. INTRODUCTION The reduction of the peak base reaction force dur- ing robot maneuvers is important for many kinds of application. These applications might be of industrial, military or research nature. Optimal motions can im- prove the life-cycle of the robot and its environment, and cost effectiveness. Additionally, minimization of the peak base reaction force reduces the impact of the robot on its environment. In a spacecraft, for example, base reaction forces are often undesired ef- fects which can be seen as a disturbance to the general * Graduate Student. Email: mjschmid@eng.buffalo.edu † Graduate Student. Email: lramrath@eng.buffalo.edu ‡ Associate Professor, Senior Member AIAA. Email: ts- ingh@eng.buffalo.edu spacecraft behavior (e.g. attitude) initiating undesired movements and oscillations. The base reaction forces of a manipulator, attached to a mobile base, can cause overturning of the base. To date, several approaches to minimize these kind of disturbances exist. If satellite manipulators are considered, most attention was paid to minimize the attitude disturbances caused by base reaction torques. Some techniques were developed which are able to min- imize the disturbance while driving the satellite back to a prescribed position (Schulz et. al 3, 4 ). Some sug- gested a partitioned approach to the control of the manipulator and the satellite. Other approaches are based on robot link motions that dynamically cancel. For a limited area in the workspace, zero base reaction force can be achieved (Papadopoulos 11 ). Only few ap- proaches to the global optimization of a manipulators peak base reaction force exist. Kazerounian and Wang used the relationship between local acceleration opti- mization and global velocity optimization. Doggett et. al 2, 5, 6 proposed a computationally efficient technique which leads to a path having a peak force within 5% of the optimal path. This approach is based on the parameterized equations of the C 2 smooth path that globally minimizes the Euclidean norm of a robot’s peak base reaction force. Additionally, Doggett et. al introduce the CM space (center of mass space), a convenient space for planning and calculating robot motions. This paper develops an approach to find the global optimal path which minimizes the robot’s peak base reaction force while avoiding obstacles in the 2-D Cartesian space. The transformation from Cartesian to CM space is used, as a multi-body robot can be transformed into a point mass simplifying path cal- 1 American Institute of Aeronautics and Astronautics