# Slew-rate Type Trajectory for Multicopters

The trajectory type can be enabled in Position mode (only) using the following parameter setting: MPC_POS_MODE=1.

MC Jerk-limited Trajectory Tuning is an alternative trajectory that provides for smoother responses.

The Slew Rate trajectory type is a simple implementation where the jerk and acceleration is limited using slew-rates (jerk and acceleration limits are not hard constraints).

It allows asymmetric profiles based on user intention (smooth acceleration and quick stop), and should be used when a quick (and potentially "jerky") response to stick input is more important than ensuring smooth acceleration and deceleration (e.g.: for aggressive flight with position hold).

This topic explains how the trajectory type can be tuned.

## Position Mode

In Position mode the stick inputs are mapped to either position-control or velocity-control.

The position controller (diagram here) consists of an outer P position-control loop and an inner PID velocity-control loop. Depending on the mode and situation either both loops are active or just the velocity control loop.

For the remainder of this topic the term position-control represents the case where both loops are active while velocity-control refers to the case when only the velocity control loop is in use.

Position-control is active when the stick inputs are within the deadzone MPC_HOLD_DZ, and velocity-control otherwise.

All the parameters below are tuning parameters and cannot be mapped directly to the physical quantity.

#### MPC_ACC_HOR_MAX

This parameter is used for position-control in the horizontal direction, where the vehicle is supposed to stay at the current location. The limit for the rate of change of the velocity setpoint is defined by MPC_ACC_HOR_MAX. This parameter should be set larger than any of the other acceleration related parameters in the horizontal direction.

#### MPC_ACC_HOR and MPC_DEC_HOR_SLOW

In velocity-control the rate limit for the velocity setpoint is extracted from a linear map from stick input to acceleration limit with maximum MPC_ACC_HOR and minimum MPC_DEC_HOR_SLOW. For example, if the stick input is at MPC_HOLD_DZ, the limiting acceleration is MPC_DEC_HOR_SLOW. If the stick input is at maximum (=1), the limiting acceleration is MPC_ACC_HOR and any stick input in between is mapped linearly between the two parameters. In addition, MPC_DEC_HOR_SLOW also limits the change in velocity setpoint when the user demands a deceleration in the current flight direction. For instance, if the stick input changes from maximum (=1) to 0.5, the velocity setpoint change will be limited by MPC_DEC_HOR_SLOW.

During transition from velocity-control to position-control, there is a hard switch from from MPC_ACC_HOR to MPC_ACC_HOR_MAX and a reset of the velocity setpoint to the current vehicle velocity. The reset and the hard switch can both introduce a jerky flight performance during stopping. Nonetheless, the reset is required because the smoothing parameters introduce a delay to the setpoint, which can lead to unexpected flight maneuvers.

A simple example explaining why the reset is needed is given below.

Consider the case where a user demands full speed from hover followed by a stop request. This is equivalent to full stick input with maximum value of 1 followed by zero stick input. To simplify the example, assume that MPC_ACC_HOR_MAX is equal to MPC_ACC_HOR and therefore there is no hard switch in acceleration limit when switching from velocity-control to position-control. In addition, let's assume the maximum speed that can be demanded is 4 m/s.

During full stick input, the velocity setpoint will not change directly from 0 m/s to 4 m/s (aka step input) - instead the velocity setpoint follows a ramp with slope MPC_ACC_HOR. The actual velocity of the vehicle, however, will not track the setpoint perfectly, but rather will lag behind. The lag will be more significant the larger the value of MPC_ACC_HOR.

Without the reset (the top graph), at the moment of the stop demand (stick equal 0) the velocity setpoint will ramp down with the maximum rate given by MPC_ACC_HOR_MAX. Due to the lag the vehicle will first continue to accelerate in the direction previous to the stop demand followed by slowly decelerating towards zero. With the reset of the velocity setpoint to the current velocity, the delay due to the lag during stop demand can be overcome.

#### MPC_ACC_UP_MAX and MPC_ACC_DOWN_MAX

MPC_ACC_UP_MAX >= MPC_ACC_DOWN_MAX, otherwise the firmware will overwrite the given values.

• position-control: the limit in velocity setpoint change in z-direction is given by MPC_ACC_UP_MAX.
• velocity-control: the limit in velocity setpoint change for stick input is MPC_ACC_UP_MAX for upward and MPC_ACC_DOWN_MAX for downward direction.

#### MPC_JERK_MAX and MPC_JERK_MIN

These two parameters only have effect during the transition from velocity-control to position-control. The purpose of these two parameters are to minimize the jerk introduced from forward flight to hover (please see MPC_ACC_HOR and MPC_DEC_HOR_SLOW).

The jerk-parameter controls the rate limit with which the acceleration limit can change to MPC_ACC_HOR_MAX. The actual jerk-value is a linear map from velocity speed to jerk where full speed maps to MPC_JERK_MAX and zero speed to MPC_JERK_MIN. The smoothing can be turned off by setting MPC_JERK_MAX to a value smaller than MPC_JERK_MIN.