VelocitySmoothing.hpp

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#pragma once

struct Trajectory {
    float j; //< jerk
    float a; //< acceleration
    float v; //< velocity
    float x; //< position
};

/**
 * @class VelocitySmoothing
 *
 * TODO: document the algorithm
 *    |T1| T2 |T3|
 *     ___
 *   __| |____   __ Jerk
 *            |_|
 *        ___
 *       /   \   Acceleration
 *   ___/     \___
 *             ___
 *           ;"
 *          /
 *         /     Velocity
 *        ;
 *   ----"
 */
class VelocitySmoothing
{
public:
    VelocitySmoothing(float initial_accel = 0.f, float initial_vel = 0.f, float initial_pos = 0.f);
    ~VelocitySmoothing() = default;

    /**
     * Reset the state.
     * @param accel Current acceleration
     * @param vel Current velocity
     * @param pos Current position
     */
    void reset(float accel, float vel, float pos);

    /**
     * Compute T1, T2, T3 depending on the current state and velocity setpoint. This should be called on every cycle
     * and before updateTraj().
     * @param vel_setpoint velocity setpoint input
     */
    void updateDurations(float vel_setpoint);

    /**
     * Generate the trajectory (acceleration, velocity and position) by integrating the current jerk
     * @param dt integration period
     * @param time_stretch (optional) used to scale the integration period. This can be used to slow down
     * or fast-forward the trajectory
     */
    void updateTraj(float dt, float time_stretch = 1.f);

    /**
     * Getters and setters
     */
    float getMaxJerk() const { return _max_jerk; }
    void setMaxJerk(float max_jerk) { _max_jerk = max_jerk; }

    float getMaxAccel() const { return _max_accel; }
    void setMaxAccel(float max_accel) { _max_accel = max_accel; }

    float getMaxVel() const { return _max_vel; }
    void setMaxVel(float max_vel) { _max_vel = max_vel; }

    float getCurrentJerk() const { return _state.j; }
    void setCurrentAcceleration(const float accel) { _state.a = _state_init.a = accel; }
    float getCurrentAcceleration() const { return _state.a; }
    void setCurrentVelocity(const float vel) { _state.v = _state_init.v = vel; }
    float getCurrentVelocity() const { return _state.v; }
    void setCurrentPosition(const float pos) { _state.x = _state_init.x = pos; }
    float getCurrentPosition() const { return _state.x; }

    float getVelSp() const { return _vel_sp; }

    float getT1() const { return _T1; }
    float getT2() const { return _T2; }
    float getT3() const { return _T3; }
    float getTotalTime() const { return _T1 + _T2 + _T3; }

    /**
     * Synchronize several trajectories to have the same total time. This is required to generate
     * straight lines.
     * The resulting total time is the one of the longest trajectory.
     * @param traj an array of VelocitySmoothing objects
     * @param n_traj the number of trajectories to be synchronized
     */
    static void timeSynchronization(VelocitySmoothing *traj, int n_traj);

private:

    /**
     * Compute T1, T2, T3 depending on the current state and velocity setpoint.
     * Minimize the total time of the trajectory
     */
    void updateDurationsMinimizeTotalTime();

    /**
     * Compute T1, T2, T3 depending on the current state and velocity setpoint.
     * @param T123 desired total time of the trajectory
     */
    void updateDurationsGivenTotalTime(float T123);

    /**
     * Compute the direction of the jerk to be applied in order to drive the current state
     * to the desired one
     */
    int computeDirection();

    /**
     * Compute the velocity at which the trajectory will be if the maximum jerk is applied
     * during the time required to cancel the current acceleration
     */
    float computeVelAtZeroAcc();

    /**
     * Compute increasing acceleration time
     */
    inline float computeT1(float a0, float v3, float j_max, float a_max);

    /**
     * Compute increasing acceleration time using total time constraint
     */
    inline float computeT1(float T123, float a0, float v3, float j_max, float a_max);

    /**
     * Saturate T1 in order to respect the maximum acceleration constraint
     */
    inline float saturateT1ForAccel(float a0, float j_max, float T1, float a_max);

    /**
     * Compute constant acceleration time
     */
    inline float computeT2(float T1, float T3, float a0, float v3, float j_max);

    /**
     * Compute constant acceleration time using total time constraint
     */
    inline float computeT2(float T123, float T1, float T3);

    /**
     * Compute decreasing acceleration time
     */
    inline float computeT3(float T1, float a0, float j_max);

    /**
     * Compute the jerk, acceleration, velocity and position
     * of a jerk-driven polynomial trajectory at a given time t
     * @param j jerk
     * @param a0 initial acceleration at t = 0
     * @param v0 initial velocity
     * @param x0 initial postion
     * @param t current time
     * @param d direction
     */
    inline Trajectory evaluatePoly(float j, float a0, float v0, float x0, float t, int d);

    /* Input */
    float _vel_sp{0.0f};

    /* Constraints */
    float _max_jerk = 22.f;
    float _max_accel = 8.f;
    float _max_vel = 6.f;

    /* State (previous setpoints) */
    Trajectory _state{};
    int _direction{0};

    /* Initial conditions */
    Trajectory _state_init{};

    /* Duration of each phase */
    float _T1 = 0.f; ///< Increasing acceleration [s]
    float _T2 = 0.f; ///< Constant acceleration [s]
    float _T3 = 0.f; ///< Decreasing acceleration [s]

    float _local_time = 0.f; ///< Current local time
};