{"id":645,"date":"2018-05-11T20:12:31","date_gmt":"2018-05-11T20:12:31","guid":{"rendered":"http:\/\/mrsdprojects.ri.cmu.edu\/2017teamc\/?page_id=645"},"modified":"2018-05-11T23:32:13","modified_gmt":"2018-05-11T23:32:13","slug":"algorithms","status":"publish","type":"page","link":"https:\/\/mrsdprojects.ri.cmu.edu\/2017teamc\/algorithms\/","title":{"rendered":"Algorithms"},"content":{"rendered":"

Emergency braking for obstacle avoidance<\/strong><\/p>\n

DJI provides Onboard SDK which can be used to communicate with DJI flight controller to receive real-time data and to control the quadcopter. Our DJI interface is built around the ros wrapper of Onboard SDK which allows receiving data as ros topics and publish commands by subscribing to ROS services.<\/span><\/p>\n

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DJI provides information related to state of the aircraft which includes position, attitude, velocity, pilot commands, etc. A separate node was written for emergency brake functionality. This node subscribes to pilot control inputs and based on position of a switch on the radio controller it either enables or disables our custom flight mode. This custom flight mode converts pilot commands to velocity commands for the quadcopter. These velocity commands are constrained if pilot\u2019s commands are leading to a collision.\u00a0<\/span><\/p>\n

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For obstacle avoidance we can easily determine the time to impact from zeroing the speed equation and introducing its value back into the position equation.<\/span><\/p>\n

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This equation can be solved for the equilibrium speed that a pilot input should give, that given a non-zero initial speed at a particular point, would stop at the obstacle location. Nonetheless, the equation is transcendent (product log) and Matlab\/Mathematica are really bad solving it (C++ is bound to be even worse).<\/span><\/p>\n

Instead of doing this, we solve for two types of situations that are really simple: the \u201cNo Return\u201d range (what is the distance the quad travels starting from a non-zero speed and having full reverse input) and the \u201cZero Input\u201d range (the distance the quad travels with a zero input when starting from a non-zero initial speed).<\/span><\/p>\n

We then fit a straight line between the two limit cases, simplifying the inverse dynamics and getting a control that reacts faster than the original function and should be more stable than a non-linear control with a function whose numerical computation is problematic. As a bonus, the straight line can be extended beyond the \u201cZero Input\u201d as we no longer have a domain problem as we did in the \u201cProduct Log\u201d. The point where we can give maximum input in the direction of the obstacle and still stop on time is referred to as \u201cFull Control\u201d.<\/span><\/p>\n

With this approach we were able to operate seamlessly in four different regimes:<\/span><\/p>\n