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A simple, robust nonlinear controller for quadcopters to avoid collisions, based on the geometry approach and kinematics equation, is proposed. The controller allows the quadcopter to avoid single and multiple obstacles. Once an obstacle with a high possibility of collision is detected, a boundary sphere of the obstacle is generated to determine the collision zone. Afterward, the tracking error angles between the quadcopter’s motion direction and the tangential lines from the quadcopter’s current position to the boundary sphere are computed to steer the direction of the quadcopter for collision avoidance. A guidance law and a velocity control law are obtained from the Lyapunov stability based on the tracking error angles and relative distances between vehicle and obstacles. In addition, a method to drive the quadcopter to the target position after the completion of collision avoidance is introduced. The effectiveness of the proposed collision-avoidance algorithm is demonstrated through the result of a numerical simulation.