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costs.ml
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open Owl
module AD = Algodiff.D
open Lib
open Defaults
open Typ
let _ = Printexc.record_backtrace true
module C_Running_4D (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye size_net *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.qs_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye size_net *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. P.t_mov)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let cost_function t = AD.Maths.(F 1. + (F 0. * t))
let q_start = Mat.(eye 2 *$ (P.qs_coeff *.0.5)) |> AD.pack_arr
let q_start_coeff = P.qs_coeff
(*AD.Maths.(
F P.alpha
* (F 1. + ((F P.beta - F 1.) * sigmoid ((t - F P.t_prep) / F 2E-3))))*)
let power u g =
AD.pack_flt
(Mat.sum' (Mat.map (fun x -> Maths.pow x g) (AD.unpack_arr (AD.primal' u))))
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in
let _dx_start = AD.Maths.(in_pos - thetas) in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques =AD.Maths.(cmc*@(phi (P.__c *@ g (transpose x_state)))) in
let start = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)) in
(* let u = AD.Maths.(u*@(transpose __b)) in *)
AD.Maths.(
((sum' (u *@ r * u) * cost_function t)
+ (sum' (dx_p *@ q * dx_p) * sigmoid ((t - tau) / F 20E-3))
+ (F 0.1 * (sum' (dx_vel *@ q * dx_vel) * sigmoid ((t - tau) / F 20E-3)))
+ (F 1. * (sum' (dx_vel *@ q_start * dx_vel) *start)
+ ( (sum' (_dx_start *@ q_start * _dx_start) * start))
+ (sum' (transpose torques *@t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3))))
* __dt)
let rl_u =
(*Need to check this*)
let rlu ~k ~x:_x ~u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let c = cost_function t in
let r = Mat.(eye size_net *$ P.r_coeff) |> AD.pack_arr in
let u = AD.Maths.(u*@(transpose P.b)) in
AD.Maths.(u *@ r*@P.b * c * __dt)
in
Some rlu
let rl_x = let rlx ~k ~x ~u:_u =
let _, x_state = unpack_full_state x 4 in
let thetas = unpack_pos x in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let start = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)) in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let __c = AD.pack_arr P.c in
let torques =AD.Maths.(cmc*@(phi (P.__c *@ g (transpose x_state)))) in
let dtorques = AD.Maths.(cmc *@ (dphi (__c*@(transpose x_state)))*@ __c) in
let dx_vel = unpack_vel x in
let dx_start = AD.Maths.(in_pos - thetas) in
let r_xstate = AD.Maths.( (transpose torques)*@ t_mat *@ dtorques * F 2. * sigmoid ((F P.t_prep - t) / F 2E-3))
in let r_xp1 = AD.Maths.(AD.F 2. * neg dx_p *@ q * sigmoid ((t - tau) / F 20E-3))
in let r_xp2 = AD.Maths.(AD.F 2. * neg dx_start *@ q_start * start)
in let r_xv1 = AD.Maths.(dx_vel *@ q * sigmoid ((t - tau) / F 20E-3) * F 0.2)
in let r_xv2 = AD.Maths.(dx_vel *@ q_start * start * F 2.)
in AD.Maths.((concatenate ~axis:1 [|r_xp1+r_xp2;r_xv1+r_xv2;r_xstate|])*__dt)
in
Some rlx
let rl_uu =
let rluu ~k ~x:_x ~u:_u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let c = cost_function t in
let ma = Mat.(eye size_net *$ P.r_coeff) |> AD.pack_arr in
AD.Maths.((transpose P.b)*@ ma*@ ( P.b) * c * __dt)
in
Some rluu
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx =
let rlxx ~k ~x:_x ~u:_u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let start = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)) in
let mu =
AD.Maths.(
(AD.Mat.eye 2 * AD.F Defaults.q_coeff * __dt * sigmoid ((t - tau) / F 20E-3))
+ (AD.F P.qs_coeff* AD.Mat.eye 2 * start * __dt))
in
let mv =
AD.Maths.(
__dt * AD.Mat.eye 2 * F Defaults.q_coeff * (F 0.1 * sigmoid ((t - tau) / F 20E-3)) +
__dt * AD.Mat.eye 2 * F P.qs_coeff * start * F 1.)
in
let mx =
AD.Maths.(
((sigmoid ((F P.t_prep - t) / F 2E-3)
* (transpose P.__c *@ t_mat* F 2. *@P.__c) )
+ (F Defaults.a_coeff * AD.Mat.eye size_net))
* __dt)
in
let mf1 =
AD.Maths.concatenate ~axis:1 [| mu; AD.Mat.zeros (n_theta - 2) (size_net + 2) |]
in
let mf2 =
AD.Maths.concatenate
~axis:1
[| AD.Mat.zeros (n_theta - 2) 2; mv; AD.Mat.zeros (n_theta - 2) size_net |]
in
let mf3 = AD.Maths.concatenate ~axis:1 [| AD.Mat.zeros size_net n_theta; mx |] in
AD.Maths.concatenate ~axis:0 [| mf1; mf2; mf3 |]
in
Some rlxx
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.((sum' (dx_p *@ q * dx_p) * F 0.) + (F 0. * sum' (dx_vel *@ q * dx_vel))))
in
fl
let fl_x = None
(*let f ~k:_k ~x:_x = AD.F 0. in
Some f*)
let fl_xx = None
end
module C_Running (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye size_net *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.qs_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye size_net *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. P.t_mov)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let cost_function t = AD.Maths.(F 1. + (F 0. * t))
let q_start = Mat.(eye 2 *$ (P.qs_coeff *.0.5)) |> AD.pack_arr
let q_start_coeff = P.qs_coeff
(*AD.Maths.(
F P.alpha
* (F 1. + ((F P.beta - F 1.) * sigmoid ((t - F P.t_prep) / F 2E-3))))*)
let power u g =
AD.pack_flt
(Mat.sum' (Mat.map (fun x -> Maths.pow x g) (AD.unpack_arr (AD.primal' u))))
let cost ~u ~x ~k =
let wp,wm = P.weighing_pm in
let cost_function t = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)*F wp + sigmoid ((t - F P.t_prep) / F 2E-4)*F wm) in
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in
let _dx_start = AD.Maths.(in_pos - thetas) in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques = AD.Maths.(P.__c *@ transpose x_state) in
let start = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)) in
let u = AD.Maths.(u*@(transpose P.b)) in
AD.Maths.(
((sum' (u *@ r * u) * cost_function t)
+ (sum' (dx_p *@ q * dx_p) * sigmoid ((t - tau) / F 20E-3))
+ (F 0.1 * (sum' (dx_vel *@ q * dx_vel) * sigmoid ((t - tau) / F 20E-3)))
+ (F 1. * (sum' (dx_vel *@ q_start * dx_vel) *start)
+ ( (sum' (_dx_start *@ q_start * _dx_start) * start))
+ (sum' (transpose torques *@t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3))))
* __dt)
let rl_u =
(*Need to check this*)
let rlu ~k ~x:_x ~u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let c = let wp,wm = P.weighing_pm in
AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)*F wp + sigmoid ((t - F P.t_prep) / F 2E-4)*F wm) in
let r = Mat.(eye size_net *$ P.r_coeff) |> AD.pack_arr in
let u = AD.Maths.(u*@(transpose P.b)) in
AD.Maths.(u *@ r*@P.b * c * __dt)
in
Some rlu
let rl_x = let rlx ~k ~x ~u:_u =
let _, x_state = unpack_full_state x 4 in
let thetas = unpack_pos x in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let start = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)) in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let __c = AD.pack_arr P.c in
let dx_vel = unpack_vel x in
let dx_start = AD.Maths.(in_pos - thetas) in
let r_xstate = AD.Maths.( x_state *@ (transpose __c)*@ t_mat *@ __c * F 2. * sigmoid ((F P.t_prep - t) / F 2E-3))
in let r_xp1 = AD.Maths.(AD.F 2. * neg dx_p *@ q * sigmoid ((t - tau) / F 20E-3))
in let r_xp2 = AD.Maths.(AD.F 2. * neg dx_start *@ q_start * start)
in let r_xv1 = AD.Maths.(dx_vel *@ q * sigmoid ((t - tau) / F 20E-3) * F 0.2)
in let r_xv2 = AD.Maths.(dx_vel *@ q_start * start * F 2.)
in AD.Maths.((concatenate ~axis:1 [|r_xp1+r_xp2;r_xv1+r_xv2;r_xstate|])*__dt)
in
Some rlx
let rl_uu =
let rluu ~k ~x:_x ~u:_u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let c = let wp,wm = P.weighing_pm in
AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)*F wp + sigmoid ((t - F P.t_prep) / F 2E-4)*F wm) in
let ma = Mat.(eye size_net *$ P.r_coeff) |> AD.pack_arr in
(AD.Maths.(P.b*@ ma*@ P.b * c * __dt))
in
Some rluu
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx =
let rlxx ~k ~x:_x ~u:_u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let start = AD.Maths.(sigmoid ((F P.t_prep - t) / F 2E-4)) in
let mu =
AD.Maths.(
(AD.Mat.eye 2 * AD.F Defaults.q_coeff * __dt * sigmoid ((t - tau) / F 20E-3))
+ (AD.F P.qs_coeff* AD.Mat.eye 2 * start * __dt))
in
let mv =
AD.Maths.(
__dt * AD.Mat.eye 2 * F Defaults.q_coeff * (F 0.1 * sigmoid ((t - tau) / F 20E-3)) +
__dt * AD.Mat.eye 2 * F P.qs_coeff * start * F 1.)
in
let mx =
AD.Maths.(
((sigmoid ((F P.t_prep - t) / F 2E-3)
* (transpose P.__c *@ t_mat* F 2. *@P.__c) )
+ (F Defaults.a_coeff * AD.Mat.eye size_net))
* __dt)
in
let mf1 =
AD.Maths.concatenate ~axis:1 [| mu; AD.Mat.zeros (n_theta - 2) (size_net + 2) |]
in
let mf2 =
AD.Maths.concatenate
~axis:1
[| AD.Mat.zeros (n_theta - 2) 2; mv; AD.Mat.zeros (n_theta - 2) size_net |]
in
let mf3 = AD.Maths.concatenate ~axis:1 [| AD.Mat.zeros size_net n_theta; mx |] in
AD.Maths.concatenate ~axis:0 [| mf1; mf2; mf3 |]
in
Some rlxx
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.((sum' (dx_p *@ q * dx_p) * F 0.) + (F 0. * sum' (dx_vel *@ q * dx_vel))))
in
fl
let fl_x = None
(*let f ~k:_k ~x:_x = AD.F 0. in
Some f*)
let fl_xx = None
end
(*
module C_End (P : Prms) = struct
let n_theta = 4
let q = Mat.(eye 2 *$ Defaults.q_coeff *$ 0.5) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (target_duration +. P.t_prep)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.)) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let tgt_vel = AD.Maths.get_slice [ []; [ 2; 3 ] ] target
let q_start = AD.F q_start
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let cost_function t = AD.Maths.(F 0. * t)
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let dx_start = AD.Maths.(in_pos - thetas) in
let _, x_state = unpack_full_state x n_theta in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques = AD.Maths.(P.__c *@ transpose x_state) in
AD.Maths.(
(sum' (u *@ r * u)
+ (q_start * (sum' (dx_start *@ q * dx_start) * sigmoid ((F P.t_prep - t) / F 2E-4)))
+ (sum' (transpose torques *@ t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3)))
* __dt)
let rl_u =
let rlu ~k:_k ~x:_x ~u =
let r = Mat.(eye P.m *$ P.r_coeff) |> AD.pack_arr in
AD.Maths.(u *@ r * __dt)
in
Some rlu
let rl_uu =
let rluu ~k:_k ~x:_x ~u:_u =
let ma = Mat.(eye P.m *$ P.r_coeff) |> AD.pack_arr in
AD.Maths.(ma * __dt)
in
Some rluu
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx =
let rlxx ~k ~x:_x ~u:_u =
let t = AD.Maths.(F (float_of_int k) * __dt) in
let mu = AD.Maths.(q_start * AD.Mat.eye 2 * sigmoid ((F P.t_prep - t) / F 2E-3)) in
let mx =
AD.Maths.(
sigmoid ((F P.t_prep - t) / F 2E-3)
* F 0.
* (transpose P.__c *@ P.__c)
* __dt)
in
let mf1 =
AD.Maths.concatenate ~axis:1 [| mu; AD.Mat.zeros (n_theta - 2) (P.m + 2) |]
in
let mf2 =
AD.Maths.concatenate
~axis:1
[| AD.Mat.zeros (n_theta - 2) 4; AD.Mat.zeros (n_theta - 2) P.m |]
in
let mf3 = AD.Maths.concatenate ~axis:1 [| AD.Mat.zeros P.m n_theta; mx |] in
AD.Maths.concatenate ~axis:0 [| mf1; mf2; mf3 |]
in
Some rlxx
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.(sum' (dx_p *@ q * dx_p) + (F 0.1 * sum' (dx_vel *@ q * dx_vel))))
in
fl
let fl_x = None
let fl_xx = None
end
module C_Successive (P : Prms) = struct
let n_theta = 4
let pause = 0.7
let q = Mat.(eye 2 *$ Defaults.q_coeff *$ 0.5) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let tau_1 = AD.F (target_duration +. P.t_prep)
let tau_2 = AD.Maths.(tau_1 + F (pause +. target_duration))
let __dt = AD.F sampling_dt
let target_1 = P.target_theta.(0) |> AD.pack_arr
let target_2 = P.target_theta.(1) |> AD.pack_arr
let tgt_pos_1 = AD.Maths.get_slice [ []; [ 0; 1 ] ] target_1
let tgt_pos_2 = AD.Maths.get_slice [ []; [ 0; 1 ] ] target_2
let cost ~u ~x ~k =
let t = AD.Maths.(F (float_of_int k) * __dt) in
let thetas = unpack_pos x in
let dx_p1 = AD.Maths.(tgt_pos_1 - thetas) in
let dx_p2 = AD.Maths.(tgt_pos_2 - thetas) in
let c1 =
AD.Maths.(
sum' (dx_p1 *@ q * dx_p1)
* sigmoid ((t - tau_1) / F 50E-3)
* sigmoid ((tau_1 + F pause - t) / F 50E-3))
and c2 = AD.Maths.(sum' (dx_p2 *@ q * dx_p2) * sigmoid ((t - tau_2) / F 50E-3)) in
AD.Maths.((sum' (u *@ r * u) + c1 + c2) * __dt)
let rl_u =
let rlu ~k:_k ~x:_x ~u =
let r = Mat.(eye P.m *$ P.r_coeff) |> AD.pack_arr in
AD.Maths.(u *@ r * __dt)
in
Some rlu
let rl_uu =
let rluu ~k:_k ~x:_x ~u:_u =
let ma = Mat.(eye P.m *$ P.r_coeff) |> AD.pack_arr in
AD.Maths.(ma * __dt)
in
Some rluu
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx =
let rlxx ~k ~x:_x ~u:_u =
let t = AD.Maths.(F (float_of_int k) * __dt) in
let mu =
AD.Maths.(
AD.Mat.(eye 2)
* ((sigmoid ((t - tau_1) / F 50E-3) * sigmoid ((tau_1 + F pause - t) / F 50E-3))
+ sigmoid ((t - tau_2) / F 50E-3)))
in
let c = AD.Maths.(F Defaults.q_coeff * __dt) in
let mf =
AD.Maths.concatenate
~axis:1
[| AD.Maths.(mu * c); AD.Mat.zeros (n_theta - 2) (P.m + 2) |]
in
AD.Maths.concatenate ~axis:0 [| mf; AD.Mat.zeros (P.m + 2) P.n |]
in
Some rlxx
let final_cost ~x:_x ~k:_k = AD.F 0.
let fl_x =
let flx ~k:_k ~x:_x = AD.F 0. in
Some flx
let fl_xx =
let flx ~k:_k ~x:_x = AD.F 0. in
Some flx
end
*)
module C_Uncertain (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (Defaults.q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F P.t_prep
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let xstar =
Mat.(
(get_slice [ [ 700 ]; [ n_theta; -1 ] ])
(load_txt "results/inputs_beg/reach_1/traj_700"))
|> AD.pack_arr
let __w = AD.pack_arr P.w
let __a = AD.Maths.((__w - AD.Mat.eye size_net)/ tau)
let __at = AD.Maths.transpose __a
let __atinv = AD.Maths.inv __at
let __ainv = AD.Maths.inv __a
let idt = AD.Mat.eye n
let a = AD.unpack_arr __a
let cost ~u ~x ~k =
let _, x_ac = unpack_full_state x n_theta in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let dx = AD.Maths.(x_ac - xstar) in
let a_of_t = Mat.(a *$ ((sampling_dt *. float k) -. P.t_prep) /$ l2norm' a) in
let at_of_t =
Mat.(transpose a *$ ((sampling_dt *. float k) -. P.t_prep) /$ l2norm' a)
in
let _expa =
if t < AD.F P.t_prep then Linalg.D.expm a_of_t |> AD.pack_arr else AD.Mat.zeros n n
in
let _expat =
if t < AD.F P.t_prep then Linalg.D.expm at_of_t |> AD.pack_arr else AD.Mat.zeros n n
in
let _ut = AD.Maths.transpose u in
let _dxt = AD.Maths.transpose dx in
let _term1 = AD.Maths.(u *@ (idt - _expa) *@ __ainv *@ _dxt) |> AD.Maths.sum' in
let _term2 = AD.Maths.(__atinv *@ (idt - _expat) *@ _dxt) |> AD.Maths.sum' in
let _term3 = AD.Maths.(sum' (u *@ r * u)) in
AD.Maths.((sqr _term1 + sqr _term2 + _term3) * __dt)
let rl_u = None
let rl_uu =
let rluu ~k:_k ~x:_x ~u:_u =
let ma = Mat.(eye P.m *$ P.r_coeff) |> AD.pack_arr in
AD.Maths.(ma * __dt)
in
Some rluu
let rl_ux = None
let rl_xx =
let rlxx ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some rlxx
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.(sum' (dx_p *@ q * dx_p) + sum' (dx_vel *@ q * dx_vel)))
in
AD.Maths.(F 1. * fl)
let fl_x = None
let fl_xx = None
end
(*
module C_Cross (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (Defaults.q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye P.m *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. target_duration)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let q_start = AD.F q_start
let gamma = AD.F P.gamma_exponent
let cost_function t = AD.Maths.(F 1. + (F 0. * t))
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in
let dx_start = AD.Maths.(in_pos - thetas) in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques = AD.Maths.(P.__c *@ transpose x_state) in
AD.Maths.(
((sum' (abs u *@ AD.Mat.ones 200 200 * abs u) * F (0.5 *. r_coeff))
(*((F r_coeff * AD.Maths.(sum' (pow (abs u) gamma)))*)
+ (sum' (dx_p *@ q * dx_p) * sigmoid ((t - tau) / F 20E-3))
+ (F 0.1 * (sum' (dx_vel *@ q * dx_vel) * sigmoid ((t - tau) / F 20E-3)))
+ (q_start * (sum' (dx_start *@ q * dx_start) * sigmoid ((F P.t_prep - t) / F 2E-4)))
+ (sum' (transpose torques *@ t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3)))
* __dt)
let rl_u =
let _rlu ~k:_k ~x:_x ~u =
AD.Maths.(F r_coeff * __dt * AD.Maths.(u *@ AD.Mat.ones 200 200))
in
None
let rl_uu =
let _rluu ~k:_k ~x:_x ~u:_u = AD.Maths.(F r_coeff * AD.Mat.ones 200 200 * __dt) in
None
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx =
let rlxx ~k ~x:_x ~u:_u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let mu =
AD.Maths.(
(AD.Mat.eye 2 * AD.F Defaults.q_coeff * __dt * sigmoid ((t - tau) / F 20E-3))
+ (q_start * AD.Mat.eye 2 * sigmoid ((F P.t_prep - t) / F 2E-4) * __dt))
in
let mv =
AD.Maths.(
__dt * AD.Mat.eye 2 * F Defaults.q_coeff * (F 0.1 * sigmoid ((t - tau) / F 20E-3)))
in
let mx =
AD.Maths.(
((sigmoid ((F P.t_prep - t) / F 2E-3)
* F P.t_coeff
* (transpose P.__c *@ P.__c))
+ (F Defaults.a_coeff * AD.Mat.eye P.m))
* __dt)
in
let mf1 =
AD.Maths.concatenate ~axis:1 [| mu; AD.Mat.zeros (n_theta - 2) (P.m + 2) |]
in
let mf2 =
AD.Maths.concatenate
~axis:1
[| AD.Mat.zeros (n_theta - 2) 2; mv; AD.Mat.zeros (n_theta - 2) P.m |]
in
let mf3 = AD.Maths.concatenate ~axis:1 [| AD.Mat.zeros P.m n_theta; mx |] in
AD.Maths.concatenate ~axis:0 [| mf1; mf2; mf3 |]
in
Some rlxx
let final_cost ~x:_x ~k:_k = AD.F 0.
let fl_x =
let f ~k:_k ~x:_x = AD.F 0. in
Some f
(*let f ~k:_k ~x:_x = AD.F 0. in
Some f*)
let fl_xx =
let f ~k:_k ~x:_x = AD.F 0. in
Some f
end
module C_Gamma (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (Defaults.q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye P.m *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. target_duration)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let q_start = AD.F q_start
let gamma = AD.F P.gamma_exponent
let cost_function t = AD.Maths.(F 0. * t)
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in
let dx_start = AD.Maths.(in_pos - thetas) in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques = AD.Maths.(P.__c *@ transpose x_state) in
AD.Maths.(
((sum' (pow (abs u) gamma) * F r_coeff)
(*((F r_coeff * AD.Maths.(sum' (pow (abs u) gamma)))*)
+ (sum' (dx_p *@ q * dx_p) * sigmoid ((t - tau) / F 20E-3))
+ (F 0.1 * (sum' (dx_vel *@ q * dx_vel) * sigmoid ((t - tau) / F 20E-3)))
+ (q_start * (sum' (dx_start *@ q * dx_start) * sigmoid ((F P.t_prep - t) / F 2E-4)))
+ (sum' (transpose torques *@ t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3)))
* __dt)
let rl_u =
let _rlu ~k:_k ~x:_x ~u =
if gamma = AD.F 1.
then AD.Maths.(F r_coeff * gamma * sum' (signum u))
else (
let u_u = AD.unpack_arr u in
let mat =
Mat.map
(fun x ->
if x < 0.
then Maths.(neg (pow (neg x) (P.gamma_exponent -. 1.)))
else Maths.(pow x (P.gamma_exponent -. 1.)))
u_u
|> AD.pack_arr
in
AD.Maths.(F r_coeff * gamma * AD.Maths.(sum' mat)))
in
None
(*Need to check this
Some rlu*)
let rl_uu =
let _rluu ~k:_k ~x:_x ~u =
if gamma = AD.F 1.
then AD.F 0.
else
AD.Maths.(
F r_coeff
* gamma
* (gamma - F 1.)
* AD.Maths.(sum' (pow (abs u) (gamma - F 2.))))
in
None
(*
let rluu ~k:_k ~x:_x ~u:_u =
AD.Maths.(F r_coeff * (gamma - F 1.) * AD.Maths.(sum' (pow u (gamma - F 1.))))
in
Some rluu*)
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx =
let rlxx ~k ~x:_x ~u:_u =
let t = AD.Maths.(__dt * F (float_of_int k)) in
let mu =
AD.Maths.(
(AD.Mat.eye 2 * AD.F Defaults.q_coeff * __dt * sigmoid ((t - tau) / F 20E-3))
+ (q_start * AD.Mat.eye 2 * sigmoid ((F P.t_prep - t) / F 2E-4) * __dt))
in
let mv =
AD.Maths.(
__dt * AD.Mat.eye 2 * F Defaults.q_coeff * (F 0.1 * sigmoid ((t - tau) / F 20E-3)))
in
let mx =
AD.Maths.(
((sigmoid ((F P.t_prep - t) / F 2E-3)
* F P.t_coeff
* (transpose P.__c *@ P.__c))
+ (F Defaults.a_coeff * AD.Mat.eye P.m))
* __dt)
in
let mf1 =
AD.Maths.concatenate ~axis:1 [| mu; AD.Mat.zeros (n_theta - 2) (P.m + 2) |]
in
let mf2 =
AD.Maths.concatenate
~axis:1
[| AD.Mat.zeros (n_theta - 2) 2; mv; AD.Mat.zeros (n_theta - 2) P.m |]
in
let mf3 = AD.Maths.concatenate ~axis:1 [| AD.Mat.zeros P.m n_theta; mx |] in
AD.Maths.concatenate ~axis:0 [| mf1; mf2; mf3 |]
in
Some rlxx
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.((F 0. * sum' (dx_p *@ q * dx_p)) + (F 0. * sum' (dx_vel *@ q * dx_vel))))
in
fl
let fl_x = None
(*let f ~k:_k ~x:_x = AD.F 0. in
Some f*)
let fl_xx = None
end
module C_Var (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (Defaults.q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye P.m *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. target_duration)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let cost_function t = AD.Maths.(F 1. + (F 0. * t))
let q_start = AD.F q_start
let power u g =
AD.pack_flt
(Mat.sum' (Mat.map (fun x -> Maths.pow x g) (AD.unpack_arr (AD.primal' u))))
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in
let dx_start = AD.Maths.(in_pos - thetas) in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques = AD.Maths.(P.__c *@ transpose x_state) in
let var = AD.Maths.(sum' (sqr (x_state - mean x_state))) in
AD.Maths.(
((sum' (u *@ r * u) / (F 1. + var))
+ sum' (x_state *@ a_mat * x_state)
+ (sum' (dx_p *@ q * dx_p) * sigmoid ((t - tau) / F 20E-3))
+ (F 0.1 * (sum' (dx_vel *@ q * dx_vel) * sigmoid ((t - tau) / F 20E-3)))
+ (q_start * (sum' (dx_start *@ q * dx_start) * sigmoid ((F P.t_prep - t) / F 2E-4)))
+ (sum' (transpose torques *@ t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3)))
* __dt)
let rl_u = None
let rl_uu = None
let rl_ux = None
let rl_xx = None
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.((sum' (dx_p *@ q * dx_p) * F 0.) + (F 0. * sum' (dx_vel *@ q * dx_vel))))
in
fl
let fl_x = None
(*let f ~k:_k ~x:_x = AD.F 0. in
Some f*)
let fl_xx = None
end
module C_Dif (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (Defaults.q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye P.m *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. target_duration)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let q_start = AD.F q_start
let gamma = AD.F P.gamma_exponent
let cost_function t = AD.Maths.(F 0. * t)
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let x_s = AD.Maths.get_slice [ []; [ 0; n - 1 ] ] x_state in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in
let dx_start = AD.Maths.(in_pos - thetas) in
let t = AD.Maths.(__dt * F (float_of_int k)) in
let torques = AD.Maths.(P.__c *@ transpose x_s) in
AD.Maths.(
((F r_coeff * AD.Maths.(sum' (sqr u)))
+ (sum' (dx_p *@ q * dx_p) * sigmoid ((t - tau) / F 20E-3))
+ (F 0.1 * (sum' (dx_vel *@ q * dx_vel) * sigmoid ((t - tau) / F 20E-3)))
+ (q_start * (sum' (dx_start *@ q * dx_start) * sigmoid ((F P.t_prep - t) / F 2E-4)))
+ (sum' (transpose torques *@ t_mat * transpose torques)
* sigmoid ((F P.t_prep - t) / F 2E-3)))
* __dt)
let rl_u = None
(*Need to check this
let rlu ~k:_k ~x:_x ~u =
AD.Maths.(F r_coeff * AD.Maths.(sum' (pow u (gamma - F 1.))))
in
Some rlu*)
let rl_uu = None
(*
let rluu ~k:_k ~x:_x ~u:_u =
AD.Maths.(F r_coeff * (gamma - F 1.) * AD.Maths.(sum' (pow u (gamma - F 1.))))
in
Some rluu*)
let rl_ux =
let f ~k:_k ~x:_x ~u:_u = AD.F 0. in
Some f
let rl_xx = None
let final_cost ~x ~k:_k =
let q = Owl.Mat.(eye 2 *$ Defaults.q_coeff) |> AD.pack_arr in
let fl =
let thetas = unpack_pos x in
let thetas_dot = unpack_vel x in
let dx_p = AD.Maths.(tgt_pos - thetas)
and dx_vel = thetas_dot in
AD.(Maths.((F 0. * sum' (dx_p *@ q * dx_p)) + (F 0. * sum' (dx_vel *@ q * dx_vel))))
in
fl
let fl_x = None
(*let f ~k:_k ~x:_x = AD.F 0. in
Some f*)
let fl_xx = None
end
module C_Ddot (P : Prms) = struct
(*default setting of qcoeff = 1E-7*)
let n_theta = 4
let q = Mat.(eye 2 *$ (Defaults.q_coeff *. 0.5)) |> AD.pack_arr
let r = Mat.(eye P.m *$ (P.r_coeff *. 0.5)) |> AD.pack_arr
let t_mat = Mat.(eye 2 *$ (P.t_coeff *. 0.5)) |> AD.pack_arr
let a_mat = Mat.(eye P.m *$ (Defaults.a_coeff *. 0.5)) |> AD.pack_arr
let tau = AD.F (P.t_prep +. target_duration)
let __dt = AD.F sampling_dt
let target = P.target_theta.(0) |> AD.pack_arr
let tgt_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] target
let in_pos = AD.Maths.get_slice [ []; [ 0; 1 ] ] initial_theta
let q_start = AD.F q_start
let gamma = AD.F P.gamma_exponent
let cost_function t = AD.Maths.(F 0. * t)
let cost ~u ~x ~k =
let thetas = unpack_pos x in
let vel = unpack_vel x in
let _, x_state = unpack_full_state x 4 in
let x_s, u_1, u_2 =
( AD.Maths.get_slice [ []; [ 0; n - 1 ] ] x_state
, AD.Maths.get_slice [ []; [ n; n + P.m - 1 ] ] x_state
, AD.Maths.get_slice [ []; [ n + P.m; -1 ] ] x_state )
in
let dx_p = AD.Maths.(tgt_pos - thetas) in
let dx_vel = vel in