[RTR] StochastiOCP merge

.gitignore

@@ -114,3 +114,6 @@ c_generated_code
 # Bioptim files
 bioptim/sandbox/
 *.pkl
+
+# Mac dev
+*.DS_store

README.md

@@ -40,6 +40,8 @@ As a tour guide that uses this binder, you can watch the `bioptim` workshop that
 - [From the sources](#installing-from-the-sources-for-linux-mac-and-windows)
 - [Installation complete](#installation-complete)
 
+[Defining our optimal control problems](#defining-our-optimal-control-problems)
+
 [A first practical example](#a-first-practical-example)
 - [The import](#the-import)
 - [Building the ocp](#building-the-ocp)
@@ -236,6 +238,19 @@ python setup.py install
 Assuming everything went well, that is it! 
 You can already enjoy bioptimizing!
 
+# Defining our optimal control problems
+Here we will detail our implementation of optimal control problems and some definitions.
+The mathematical transcription of the OCP is as follows:
+![](OCP_equation.png)
+The optimization variables are the states (x = variables that represent the state of the system at each node and that 
+are subject to continuity constraints), controls (u = decision variables defined at each node that have an effect on the system),
+algebraic states (s = optimization variables that are defined at each node, but that are not subject to the 
+built-in continuity constraints), and parameters (p = optimization variables that are defined once per phase).
+The state continuity constraints implementation may vary depending on the transcription of the problem (implicit vs explicit, direct multiple shooting vs direct collocations).
+
+The cost function can include Mayer terms (function evaluated at one node) and Lagrange terms (functions integrated over the duration of the phase).
+The optimization variables can be subject to equality and/or inequality constraints.
+
 # A first practical example
 The easiest way to learn `bioptim` is to dive into it.
 So let's do that and build our first optimal control program together.

bioptim/__init__.py

@@ -220,4 +220,6 @@
 from .optimization.variable_scaling import VariableScalingList, VariableScaling
 from .optimization.variational_optimal_control_program import VariationalOptimalControlProgram
 
+from .optimization.stochastic_optimal_control_program import StochasticOptimalControlProgram
+from .optimization.problem_type import SocpType
 from .misc.casadi_expand import lt, le, gt, ge, if_else, if_else_zero

bioptim/dynamics/dynamics_functions.py

@@ -42,7 +42,9 @@ class DynamicsFunctions:
     """
 
     @staticmethod
-    def custom(states: MX.sym, controls: MX.sym, parameters: MX.sym, nlp) -> DynamicsEvaluation:
+    def custom(
+        states: MX.sym, controls: MX.sym, parameters: MX.sym, stochastic_variables: MX.sym, nlp
+    ) -> DynamicsEvaluation:
         """
         Interface to custom dynamic function provided by the user.
 
@@ -65,13 +67,14 @@ def custom(states: MX.sym, controls: MX.sym, parameters: MX.sym, nlp) -> Dynamic
             The defects of the implicit dynamics
         """
 
-        return nlp.dynamics_type.dynamic_function(states, controls, parameters, nlp)
+        return nlp.dynamics_type.dynamic_function(states, controls, parameters, stochastic_variables, nlp)
 
     @staticmethod
     def torque_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         with_contact: bool,
         with_passive_torque: bool,
@@ -227,6 +230,7 @@ def torque_activations_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         with_contact: bool,
         with_passive_torque: bool,
@@ -285,6 +289,7 @@ def torque_derivative_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         rigidbody_dynamics: RigidBodyDynamics,
         with_contact: bool,
@@ -355,6 +360,7 @@ def forces_from_torque_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         with_passive_torque: bool = False,
         with_ligament: bool = False,
@@ -370,6 +376,8 @@ def forces_from_torque_driven(
             The controls of the system
         parameters: MX.sym
             The parameters of the system
+        stochastic_variables: MX.sym
+            The stochastic variables of the system
         nlp: NonLinearProgram
             The definition of the system
         with_passive_torque: bool
@@ -400,6 +408,7 @@ def forces_from_torque_activation_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         with_passive_torque: bool = False,
         with_ligament: bool = False,
@@ -445,6 +454,7 @@ def muscles_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         with_contact: bool,
         with_passive_torque: bool = False,
@@ -580,6 +590,7 @@ def forces_from_muscle_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         with_passive_torque: bool = False,
         with_ligament: bool = False,
@@ -626,6 +637,7 @@ def joints_acceleration_driven(
         states: MX.sym,
         controls: MX.sym,
         parameters: MX.sym,
+        stochastic_variables: MX.sym,
         nlp,
         rigidbody_dynamics: RigidBodyDynamics = RigidBodyDynamics.ODE,
     ) -> DynamicsEvaluation:
@@ -892,6 +904,7 @@ def holonomic_torque_driven(
         states: MX | SX,
         controls: MX | SX,
         parameters: MX | SX,
+        stochastic_variables: MX | SX,
         nlp: NonLinearProgram,
     ) -> DynamicsEvaluation:
         """
@@ -905,6 +918,8 @@ def holonomic_torque_driven(
             The controls of the system
         parameters: MX | SX
             The parameters acting on the system
+        stochastic_variables: MX | SX
+            The stochastic variables of the system
         nlp: NonLinearProgram
             A reference to the phase