feat: 第一次提交

Improve Docstrings

.idea/.gitignore

@@ -0,0 +1,8 @@
+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml

.idea/inspectionProfiles/Project_Default.xml

@@ -0,0 +1,15 @@
+<component name="InspectionProjectProfileManager">
+  <profile version="1.0">
+    <option name="myName" value="Project Default" />
+    <inspection_tool class="PyCompatibilityInspection" enabled="true" level="WARNING" enabled_by_default="true">
+      <option name="ourVersions">
+        <value>
+          <list size="2">
+            <item index="0" class="java.lang.String" itemvalue="3.9" />
+            <item index="1" class="java.lang.String" itemvalue="3.11" />
+          </list>
+        </value>
+      </option>
+    </inspection_tool>
+  </profile>
+</component>

.idea/inspectionProfiles/profiles_settings.xml

@@ -0,0 +1,6 @@
+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

.idea/misc.xml

@@ -0,0 +1,10 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="Python 3.12 (mpc_python12)" />
+  </component>
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.12 (mpc_python12)" project-jdk-type="Python SDK" />
+  <component name="PythonCompatibilityInspectionAdvertiser">
+    <option name="version" value="3" />
+  </component>
+</project>

.idea/modules.xml

@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/mpc_python.iml" filepath="$PROJECT_DIR$/.idea/mpc_python.iml" />
+    </modules>
+  </component>
+</project>

.idea/mpc_python.iml

@@ -0,0 +1,14 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$">
+      <excludeFolder url="file://$MODULE_DIR$/venv" />
+    </content>
+    <orderEntry type="jdk" jdkName="Python 3.12 (mpc_python12)" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="PyDocumentationSettings">
+    <option name="format" value="PLAIN" />
+    <option name="myDocStringFormat" value="Plain" />
+  </component>
+</module>

.idea/vcs.xml

@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="" vcs="Git" />
+  </component>
+</project>

README.md

@@ -9,12 +9,12 @@ This mainly uses **[CVXPY](https://www.cvxpy.org/)** as a framework. This repo c
 
 * To run the pybullet demo:
 ```bash
-python3 mpc_demo_pybullet.py
+python3 ./mpc_pybullet_demo/mpc_demo_pybullet.py
 ```
 
 * To run the simulation-less demo (simpler demo that does not use pybullet, useful for debugging):
 ```bash
-python3 mpc_demo_pybullet.py
+python3 ./mpc_pybullet_demo/mpc_demo_nosim.py
 ```
 
 In both cases the script will promt the user for `enter` before starting the demo.

mpc_pybullet_demo/cvxpy_mpc/cvxpy_mpc.py

@@ -10,15 +10,16 @@ class MPC:
         self, vehicle, T, DT, state_cost, final_state_cost, input_cost, input_rate_cost
     ):
         """
-        :param vehicle:
-        :param T:
-        :param DT:
-        :param state_cost:
-        :param final_state_cost:
-        :param input_cost:
-        :param input_rate_cost:
-        """
 
+        Args:
+            vehicle ():
+            T ():
+            DT ():
+            state_cost ():
+            final_state_cost ():
+            input_cost ():
+            input_rate_cost ():
+        """
         self.nx = 4  # number of state vars
         self.nu = 2  # umber of input/control vars
 
@@ -43,10 +44,14 @@ class MPC:
 
     def get_linear_model_matrices(self, x_bar, u_bar):
         """
-        Computes the LTI approximated state space model x' = Ax + Bu + C
+        Computes the approximated LTI state space model x' = Ax + Bu + C
-        :param x_bar:
+
-        :param u_bar:
+        Args:
-        :return:
+            x_bar (array-like):
+            u_bar (array-like):
+
+        Returns:
+
         """
 
         x = x_bar[0]
@@ -96,46 +101,51 @@ class MPC:
         verbose=False,
     ):
         """
-        Optimisation problem defined for the linearised model,
+
-        :param initial_state:
+        Args:
-        :param target:
+            initial_state (array-like): current estimate of [x, y, v, heading]
-        :param verbose:
+            target (ndarray): state space reference, in the same frame as the provided current state
-        :return:
+            prev_cmd (array-like): previous [acceleration, steer]. note this is used in bounds and has to be realistic.
+            verbose (bool):
+
+        Returns:
+
         """
-
         assert len(initial_state) == self.nx
+        assert len(prev_cmd) == self.nu
+        assert target.shape == (self.nx, self.control_horizon)
 
-        # Create variables
+        # Create variables needed for setting up cvxpy problem
         x = opt.Variable((self.nx, self.control_horizon + 1), name="states")
         u = opt.Variable((self.nu, self.control_horizon), name="actions")
         cost = 0
         constr = []
 
+        # NOTE: here the state linearization is performed around the starting condition to simplify the controller.
+        # This approximation gets more inaccurate as the controller looks at the future.
+        # To improve performance we can keep track of previous optimized x, u and compute these matrices for each timestep k
+        # Ak, Bk, Ck = self.get_linear_model_matrices(x_prev[:,k], u_prev[:,k])
         A, B, C = self.get_linear_model_matrices(initial_state, prev_cmd)
 
+        # Tracking error cost
+        for k in range(self.control_horizon):
+            cost += opt.quad_form(x[:, k + 1] - target[:, k], self.Q)
+
+        # Final point tracking cost
+        cost += opt.quad_form(x[:, -1] - target[:, -1], self.Qf)
+
+        # Actuation magnitude cost
         for k in range(self.control_horizon):
-            cost += opt.quad_form(target[:, k] - x[:, k + 1], self.Q)
             cost += opt.quad_form(u[:, k], self.R)
 
-            # Actuation rate of change
+        # Actuation rate of change cost
-            if k < (self.control_horizon - 1):
+        for k in range(1, self.control_horizon):
-                cost += opt.quad_form(u[:, k + 1] - u[:, k], self.P)
+            cost += opt.quad_form(u[:, k] - u[:, k - 1], self.P)
 
-            # Kinematics Constrains
+        # Kinematics Constrains
+        for k in range(self.control_horizon):
             constr += [x[:, k + 1] == A @ x[:, k] + B @ u[:, k] + C]
 
-            # Actuation rate of change bounds
-            if k < (self.control_horizon - 1):
-                constr += [
-                    opt.abs(u[0, k + 1] - u[0, k]) / self.dt <= self.vehicle.max_d_acc
-                ]
-                constr += [
-                    opt.abs(u[1, k + 1] - u[1, k]) / self.dt <= self.vehicle.max_d_steer
-                ]
-
-        # Final Point tracking
-        cost += opt.quad_form(x[:, -1] - target[:, -1], self.Qf)
-
         # initial state
         constr += [x[:, 0] == initial_state]
 
@@ -143,6 +153,17 @@ class MPC:
         constr += [opt.abs(u[:, 0]) <= self.vehicle.max_acc]
         constr += [opt.abs(u[:, 1]) <= self.vehicle.max_steer]
 
+        # Actuation rate of change bounds
+        constr += [opt.abs(u[0, 0] - prev_cmd[0]) / self.dt <= self.vehicle.max_d_acc]
+        constr += [opt.abs(u[1, 0] - prev_cmd[1]) / self.dt <= self.vehicle.max_d_steer]
+        for k in range(1, self.control_horizon):
+            constr += [
+                opt.abs(u[0, k] - u[0, k - 1]) / self.dt <= self.vehicle.max_d_acc
+            ]
+            constr += [
+                opt.abs(u[1, k] - u[1, k - 1]) / self.dt <= self.vehicle.max_d_steer
+            ]
+
         prob = opt.Problem(opt.Minimize(cost), constr)
         solution = prob.solve(solver=opt.OSQP, warm_start=True, verbose=False)
         return x, u

mpc_pybullet_demo/cvxpy_mpc/utils.py

@@ -4,11 +4,14 @@ from scipy.interpolate import interp1d
 
 def compute_path_from_wp(start_xp, start_yp, step=0.1):
     """
-    Computes a reference path given a set of waypoints
+
-    :param start_xp:
+    Args:
-    :param start_yp:
+        start_xp (array-like): 1D array of x-positions
-    :param step:
+        start_yp (array-like): 1D array of y-positions
-    :return:
+        step (float): intepolation step
+
+    Returns:
+        ndarray of shape (3,N) representing the  path as x,y,heading
     """
     final_xp = []
     final_yp = []
@@ -34,10 +37,14 @@ def compute_path_from_wp(start_xp, start_yp, step=0.1):
 
 def get_nn_idx(state, path):
     """
-    Computes the index of the waypoint closest to vehicle
+    Finds the index of the closest element
-    :param state:
+
-    :param path:
+    Args:
-    :return:
+        state (array-like): 1D array whose first two elements are x-pos and y-pos
+        path (ndarray): 2D array of shape (2,N) of x,y points
+
+    Returns:
+        int: the index of the closest element
     """
     dx = state[0] - path[0, :]
     dy = state[1] - path[1, :]
@@ -61,11 +68,17 @@ def get_nn_idx(state, path):
 
 def get_ref_trajectory(state, path, target_v, T, DT):
     """
-    Reinterpolate the trajectory to get a set N desired target states
+
-    :param state:
+    Args:
-    :param path:
+        state (array-like): state of the vehicle in global frame
-    :param target_v:
+        path (ndarray): 2D array representing the path as x,y,heading points in global frame
-    :return:
+        target_v (float): desired speed
+        T (float): control horizon duration
+        DT (float):  control horizon time-step
+
+    Returns:
+        ndarray: 2D array representing state space trajectory [x_k, y_k, v_k, theta_k] w.r.t ego frame.
+        Interpolated according to the time-step and the desired velocity
     """
     K = int(T / DT)
 
@@ -89,7 +102,7 @@ def get_ref_trajectory(state, path, target_v, T, DT):
     stop_idx = np.where(xref_cdist == cdist[-1])
     xref[2, stop_idx] = 0.0
 
-    # transform in car ego frame
+    # transform in ego frame
     dx = xref[0, :] - state[0]
     dy = xref[1, :] - state[1]
     xref[0, :] = dx * np.cos(-state[3]) - dy * np.sin(-state[3])  # X
@@ -98,7 +111,14 @@ def get_ref_trajectory(state, path, target_v, T, DT):
 
     def fix_angle_reference(angle_ref, angle_init):
         """
-        This function returns a "smoothened" angle_ref wrt angle_init so there are no jumps.
+        Removes jumps greater than 2PI to smooth the heading
+
+        Args:
+            angle_ref (array-like):
+            angle_init (float):
+
+        Returns:
+            array-like:
         """
         diff_angle = angle_ref - angle_init
         diff_angle = np.unwrap(diff_angle)

mpc_pybullet_demo/cvxpy_mpc/vehicle_model.py

@@ -3,13 +3,21 @@ import numpy as np
 
 class VehicleModel:
     """
-    Helper class to hold vehicle info
+    Helper class that contains the parameters of the vehicle to be controlled
+
+    Attributes:
+        wheelbase: [m]
+        max_speed: [m/s]
+        max_acc: [m/ss]
+        max_d_acc: [m/sss]
+        max_steer: [rad]
+        max_d_steer: [rad/s]
     """
 
     def __init__(self):
-        self.wheelbase = 0.3  # vehicle wheelbase [m]
+        self.wheelbase = 0.3
-        self.max_speed = 1.5  # [m/s]
+        self.max_speed = 1.5
-        self.max_acc = 1.0  # [m/ss]
+        self.max_acc = 1.0
-        self.max_d_acc = 1.0  # [m/sss]
+        self.max_d_acc = 1.0
-        self.max_steer = np.radians(30)  # [rad]
+        self.max_steer = np.radians(30)
-        self.max_d_steer = np.radians(30)  # [rad/s]
+        self.max_d_steer = np.radians(30)

mpc_pybullet_demo/mpc_demo_nosim.py

@@ -27,33 +27,29 @@ L = 0.3  # vehicle wheelbase [m]
 # Classes
 class MPCSim:
     def __init__(self):
-        # State for the robot mathematical model [x,y,heading]
+        # State of the robot [x,y,v, heading]
         self.state = np.array([SIM_START_X, SIM_START_Y, SIM_START_V, SIM_START_H])
 
-        # starting guess
+        # helper variable to keep track of mpc output
-        self.action = np.zeros(2)
+        # starting condition is 0,0
-        self.action[0] = 1.0  # a
+        self.control = np.zeros(2)
-        self.action[1] = 0.0  # delta
 
         self.K = int(T / DT)
-        self.opt_u = np.zeros((2, self.K))
 
-        # Weights for Cost Matrices
         Q = [20, 20, 10, 20]  # state error cost
         Qf = [30, 30, 30, 30]  # state final error cost
         R = [10, 10]  # input cost
         P = [10, 10]  # input rate of change cost
-
         self.mpc = MPC(VehicleModel(), T, DT, Q, Qf, R, P)
 
-        # Interpolated Path to follow given waypoints
+        # Path from waypoint interpolation
         self.path = compute_path_from_wp(
             [0, 3, 4, 6, 10, 12, 13, 13, 6, 1, 0],
             [0, 0, 2, 4, 3, 3, -1, -2, -6, -2, -2],
             0.05,
         )
 
-        # Sim help vars
+        # Helper variables to keep track of the sim
         self.sim_time = 0
         self.x_history = []
         self.y_history = []
@@ -61,7 +57,7 @@ class MPCSim:
         self.h_history = []
         self.a_history = []
         self.d_history = []
-        self.predicted = None
+        self.optimized_trajectory = None
 
         # Initialise plot
         plt.style.use("ggplot")
@@ -69,24 +65,26 @@ class MPCSim:
         plt.ion()
         plt.show()
 
-    def preview(self, mpc_out):
+    def ego_to_global(self, mpc_out):
         """
-        [TODO:summary]
+        transforms optimized trajectory XY points from ego(car) reference
+        into global(map) frame
 
-        [TODO:description]
+        Args:
+            mpc_out ():
         """
-        predicted = np.zeros(self.opt_u.shape)
+        trajectory = np.zeros((2, self.K))
-        predicted[:, :] = mpc_out[0:2, 1:]
+        trajectory[:, :] = mpc_out[0:2, 1:]
         Rotm = np.array(
             [
                 [np.cos(self.state[3]), np.sin(self.state[3])],
                 [-np.sin(self.state[3]), np.cos(self.state[3])],
             ]
         )
-        predicted = (predicted.T.dot(Rotm)).T
+        trajectory = (trajectory.T.dot(Rotm)).T
-        predicted[0, :] += self.state[0]
+        trajectory[0, :] += self.state[0]
-        predicted[1, :] += self.state[1]
+        trajectory[1, :] += self.state[1]
-        self.predicted = predicted
+        return trajectory
 
     def run(self):
         """
@@ -109,31 +107,31 @@ class MPCSim:
                 return
             # optimization loop
             # start=time.time()
-            # dynamycs w.r.t robot frame
+
-            curr_state = np.array([0, 0, self.state[2], 0])
             # Get Reference_traj -> inputs are in worldframe
             target = get_ref_trajectory(self.state, self.path, TARGET_VEL, T, DT)
 
+            # dynamycs w.r.t robot frame
+            curr_state = np.array([0, 0, self.state[2], 0])
             x_mpc, u_mpc = self.mpc.step(
                 curr_state,
                 target,
-                self.action,
+                self.control,
                 verbose=False,
             )
-            # NOTE: used only for preview purposes
-            self.opt_u = np.vstack(
-                (
-                    np.array(u_mpc.value[0, :]).flatten(),
-                    np.array(u_mpc.value[1, :]).flatten(),
-                )
-            )
-            self.action[:] = [u_mpc.value[0, 0], u_mpc.value[1, 0]]
             # print("CVXPY Optimization Time: {:.4f}s".format(time.time()-start))
-            self.predict([self.action[0], self.action[1]], DT)
+            # only the first one is used to advance the simulation
-            self.preview(x_mpc.value)
+
+            self.control[:] = [u_mpc.value[0, 0], u_mpc.value[1, 0]]
+            self.state = self.predict_next_state(
+                self.state, [self.control[0], self.control[1]], DT
+            )
+
+            # use the optimizer output to preview the predicted state trajectory
+            self.optimized_trajectory = self.ego_to_global(x_mpc.value)
             self.plot_sim()
 
-    def predict(self, u, dt):
+    def predict_next_state(self, state, u, dt):
         def kinematics_model(x, t, u):
             dxdt = x[2] * np.cos(x[3])
             dydt = x[2] * np.sin(x[3])
@@ -144,21 +142,17 @@ class MPCSim:
 
         # solve ODE
         tspan = [0, dt]
-        self.state = odeint(kinematics_model, self.state, tspan, args=(u[:],))[1]
+        new_state = odeint(kinematics_model, state, tspan, args=(u[:],))[1]
+        return new_state
 
     def plot_sim(self):
-        """
-        [TODO:summary]
-
-        [TODO:description]
-        """
         self.sim_time = self.sim_time + DT
         self.x_history.append(self.state[0])
         self.y_history.append(self.state[1])
         self.v_history.append(self.state[2])
         self.h_history.append(self.state[3])
-        self.a_history.append(self.opt_u[0, 1])
+        self.a_history.append(self.control[0])
-        self.d_history.append(self.opt_u[1, 1])
+        self.d_history.append(self.control[1])
 
         plt.clf()
 
@@ -186,10 +180,10 @@ class MPCSim:
             label="vehicle trajectory",
         )
 
-        if self.predicted is not None:
+        if self.optimized_trajectory is not None:
             plt.plot(
-                self.predicted[0, :],
+                self.optimized_trajectory[0, :],
-                self.predicted[1, :],
+                self.optimized_trajectory[1, :],
                 c="tab:green",
                 marker="+",
                 alpha=0.5,
@@ -246,18 +240,11 @@ class MPCSim:
 
 def plot_car(x, y, yaw):
     """
-    [TODO:summary]
 
-    [TODO:description]
+    Args:
-
+        x ():
-    Parameters
+        y ():
-    ----------
+        yaw ():
-    x : [TODO:type]
-        [TODO:description]
-    y : [TODO:type]
-        [TODO:description]
-    yaw : [TODO:type]
-        [TODO:description]
     """
     LENGTH = 0.5  # [m]
     WIDTH = 0.25  # [m]

mpc_pybullet_demo/mpc_demo_pybullet.py

@@ -18,7 +18,14 @@ DT = 0.2  # discretization step [s]
 
 
 def get_state(robotId):
-    """ """
+    """
+
+    Args:
+        robotId ():
+
+    Returns:
+
+    """
     robPos, robOrn = p.getBasePositionAndOrientation(robotId)
     linVel, angVel = p.getBaseVelocity(robotId)
 
@@ -33,6 +40,14 @@ def get_state(robotId):
 
 
 def set_ctrl(robotId, currVel, acceleration, steeringAngle):
+    """
+
+    Args:
+        robotId ():
+        currVel ():
+        acceleration ():
+        steeringAngle ():
+    """
     gearRatio = 1.0 / 21
     steering = [0, 2]
     wheels = [8, 15]
@@ -56,7 +71,6 @@ def set_ctrl(robotId, currVel, acceleration, steeringAngle):
 
 
 def plot_results(path, x_history, y_history):
-    """ """
     plt.style.use("ggplot")
     plt.figure()
     plt.title("MPC Tracking Results")
@@ -78,7 +92,6 @@ def plot_results(path, x_history, y_history):
 
 
 def run_sim():
-    """ """
     p.connect(p.GUI)
     p.resetDebugVisualizerCamera(
         cameraDistance=1.0,
@@ -213,10 +226,8 @@ def run_sim():
     for x_, y_ in zip(path[0, :], path[1, :]):
         p.addUserDebugLine([x_, y_, 0], [x_, y_, 0.33], [0, 0, 1])
 
-    # starting guess
+    # starting conditions
-    action = np.zeros(2)
+    control = np.zeros(2)
-    action[0] = 1.0  # a
-    action[1] = 0.0  # delta
 
     # Cost Matrices
     Q = [20, 20, 10, 20]  # state error cost [x,y,v,yaw]
@@ -260,21 +271,21 @@ def run_sim():
         # simulate one timestep actuation delay
         ego_state[0] = ego_state[0] + ego_state[2] * np.cos(ego_state[3]) * DT
         ego_state[1] = ego_state[1] + ego_state[2] * np.sin(ego_state[3]) * DT
-        ego_state[2] = ego_state[2] + action[0] * DT
+        ego_state[2] = ego_state[2] + control[0] * DT
-        ego_state[3] = ego_state[3] + action[0] * np.tan(action[1]) / L * DT
+        ego_state[3] = ego_state[3] + control[0] * np.tan(control[1]) / L * DT
 
         # optimization loop
         start = time.time()
 
         # MPC step
-        _, u_mpc = mpc.step(ego_state, target, action, verbose=False)
+        _, u_mpc = mpc.step(ego_state, target, control, verbose=False)
-        action[0] = u_mpc.value[0, 0]
+        control[0] = u_mpc.value[0, 0]
-        action[1] = u_mpc.value[1, 0]
+        control[1] = u_mpc.value[1, 0]
 
         elapsed = time.time() - start
         print("CVXPY Optimization Time: {:.4f}s".format(elapsed))
 
-        set_ctrl(car, state[2], action[0], action[1])
+        set_ctrl(car, state[2], control[0], control[1])
 
         if DT - elapsed > 0:
             time.sleep(DT - elapsed)

notebooks/1.0-lti-system-modelling.ipynb

@@ -11,9 +11,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
-   "metadata": {},
+   "metadata": {
-   "outputs": [],
+    "ExecuteTime": {
+     "end_time": "2024-10-22T08:05:56.118290Z",
+     "start_time": "2024-10-22T08:05:46.550696Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Matplotlib is building the font cache; this may take a moment.\n"
+     ]
+    }
+   ],
    "source": [
     "import numpy as np\n",
     "from scipy.integrate import odeint\n",
@@ -177,8 +190,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 3,
-   "metadata": {},
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-10-22T08:06:14.547915Z",
+     "start_time": "2024-10-22T08:06:14.544585Z"
+    }
+   },
    "outputs": [],
    "source": [
     "# Define process model\n",
@@ -220,15 +238,23 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
-   "metadata": {},
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2024-10-22T08:06:17.956990Z",
+     "start_time": "2024-10-22T08:06:17.847071Z"
+    }
+   },
    "outputs": [
     {
-     "name": "stdout",
+     "ename": "NameError",
-     "output_type": "stream",
+     "evalue": "name 'M' is not defined",
-     "text": [
+     "output_type": "error",
-      "CPU times: user 3.39 ms, sys: 0 ns, total: 3.39 ms\n",
+     "traceback": [
-      "Wall time: 2.79 ms\n"
+      "\u001B[0;31m---------------------------------------------------------------------------\u001B[0m",
+      "\u001B[0;31mNameError\u001B[0m                                 Traceback (most recent call last)",
+      "File \u001B[0;32m<timed exec>:1\u001B[0m\n",
+      "\u001B[0;31mNameError\u001B[0m: name 'M' is not defined"
      ]
     }
    ],
@@ -443,9 +469,9 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda env:.conda-jupyter] *",
+   "name": "python3",
    "language": "python",
-   "name": "conda-env-.conda-jupyter-py"
+   "display_name": "Python 3 (ipykernel)"
   },
   "language_info": {
    "codemirror_mode": {

requirements.txt

@@ -1,6 +1,6 @@
-pybullet==2.7.2
+pybullet>=2.7.2
-cvxpy==1.0.28
+cvxpy>=1.0.28
 dccp
 numpy>=1.22
-osqp==0.6.1
+osqp>=0.6.1
-scipy==1.10.0
+scipy>=1.10.0